Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 21 Jan 2013
Posts: 6
Location: India
WE: Engineering (Telecommunications)

ABC is a right angled triangle with BC=6cm and AB=8 cm [#permalink]
Show Tags
18 Jan 2014, 07:52
Question Stats:
64% (01:42) correct 36% (02:00) wrong based on 220 sessions
HideShow timer Statistics
ABC is a right angled triangle with BC = 6 cm and AB = 8 cm. AC is hypotenuse. A circle with centre O and radius x has been inscribed. What is the value of x. A. 2.4 cm B. 2 cm C. 3.6 cm D. 4 cm E. 3 cm Attachment:
1796929.png [ 6.54 KiB  Viewed 97583 times ]
Official Answer and Stats are available only to registered users. Register/ Login.



Manager
Joined: 23 Jun 2008
Posts: 85
Location: Australia
GMAT Date: 04012014

Re: ABC is a right angled triangle with BC=6cm and AB=8 cm [#permalink]
Show Tags
19 Jan 2014, 15:28
005ashok wrote: ABC is a right angled triangle with BC=6cm and AB=8 cm. AC is hypotenuse. A circle with centre O and radius x has been inscribed. What is the value of x.
a. 2.4 cm b.2 cm c.3.6 cm d.4 cm e.3 cm Answer is 2. detailed explanation is given here: http://mathforum.org/library/drmath/view/54670.html
_________________
Kudos (+1) if you find this post helpful.



SVP
Joined: 14 Apr 2009
Posts: 2189
Location: New York, NY

Re: ABC is a right angled triangle with BC=6cm and AB=8 cm [#permalink]
Show Tags
19 Jan 2014, 18:24
005ashok wrote: ABC is a right angled triangle with BC=6cm and AB=8 cm. AC is hypotenuse. A circle with centre O and radius x has been inscribed. What is the value of x.
a. 2.4 cm b.2 cm c.3.6 cm d.4 cm e.3 cm Once you have circle inscribed into that triangle  you'll notice you won't have the traditional tips to solve this question. This is a 345 triangle but the angles are not the typical 306090 degree triangle. Instead you have so solve for r  radius. The way to solve this is to draw a line from radius to all 3 vertices  so you have 3 separate lines. This creates OA, OB, and OC and 3 smaller triangles within the larger 6810 triangle. THe sum of the 3 smaller triangles should equal the sum of the large triangle. The reason we care about the smaller triangles is because we know their "height" is going to be "r". So 1/2 * base * height, the height will be r. 1/2 * 6* r + 1/2 * 8 * r + 1/2 * 10 * r = 1/2 * 8 * 6 12r = 24 r = 2



Manager
Joined: 21 Jun 2014
Posts: 138
Location: United States
Concentration: General Management, Strategy
GPA: 3.4
WE: Engineering (Computer Software)

Re: ABC is a right angled triangle with BC=6cm and AB=8 cm [#permalink]
Show Tags
06 Jul 2015, 08:12
This is a right angled triangle with sides 6 and 8 .Third side will be 10(Pythagorean triplets) . The circle is inscribed in the triangle . So all the three sides are at tangent to the circle .A line drawn from center of the circle will be perpendicular to the sides of the triangle Area of triangle :6*8=48 The larger triangle can be broken into three smaller triangles with base =8,height=r ,base=10,height=r ,base 6 height=r . Sum of areas of these three triangle :8r+10r+6r=24r .24r=48 ,hence r=2 .Option B Regards, Manish Khare
_________________
Regards, Manish Khare "Every thing is fine at the end. If it is not fine ,then it is not the end "



Senior Manager
Joined: 27 Dec 2013
Posts: 279

Re: ABC is a right angled triangle with BC=6cm and AB=8 cm [#permalink]
Show Tags
06 Jul 2015, 10:39
Hi All, My answer is 1.92 (The closest answer is 2) My work as follows. The area of the right triangle should be same which ever be the base. 1/2 * 8 *6= 1/2 * 10 * h (h= the altitube drawn to the hypotenuse) h= 4.8. h= BO+ OP. B0 = sqrt 2 * r (diagnoal of a square) OP= r= Radius. sqrt 2 * r + r= 4.8== r = 1.92 Please let me know whether I am correct. 005ashok wrote: Attachment: 1796929.png ABC is a right angled triangle with BC = 6 cm and AB = 8 cm. AC is hypotenuse. A circle with centre O and radius x has been inscribed. What is the value of x. A. 2.4 cm B. 2 cm C. 3.6 cm D. 4 cm E. 3 cm
_________________
Kudos to you, for helping me with some KUDOS.



Intern
Joined: 01 Jun 2013
Posts: 8

Re: ABC is a right angled triangle with BC=6cm and AB=8 cm [#permalink]
Show Tags
27 Dec 2015, 10:22
The formula for r is when circle is inscribed in right triangle is  Perpendicular+basehypotenuses =2 r Let me know if someone wants to know the derivation.



BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2642
GRE 1: 323 Q169 V154

Re: ABC is a right angled triangle with BC=6cm and AB=8 cm [#permalink]
Show Tags
03 Apr 2016, 22:06
There are two ways as far as i know i will use the area formula as that is more likely to hit my mind first although the rule states that for any circle to be inscribed in an 90 triangle => the radius => P+B H/2 where P,B,H are three sides of the triangle and H being the largest
_________________
MBA Financing: INDIAN PUBLIC BANKS vs PRODIGY FINANCE! Getting into HOLLYWOOD with an MBA! The MOST AFFORDABLE MBA programs!STONECOLD's BRUTAL Mock Tests for GMATQuant(700+)AVERAGE GRE Scores At The Top Business Schools!



Intern
Joined: 09 Jun 2017
Posts: 49

Re: ABC is a right angled triangle with BC=6cm and AB=8 cm [#permalink]
Show Tags
Updated on: 03 May 2018, 05:33
Quote: Hi All,
My answer is 1.92 (The closest answer is 2)
My work as follows.
The area of the right triangle should be same which ever be the base.
1/2 * 8 *6= 1/2 * 10 * h (h= the altitube drawn to the hypotenuse)
h= 4.8.
h= BO+ OP.
B0 = sqrt 2 * r (diagnoal of a square)
OP= r= Radius.
sqrt 2 * r + r= 4.8== r = 1.92
Please let me know whether I am correct.
I don' think you're completely correct . you assumed that the altitude drawn from B to AC , and the bisector of angle A are the same line . This is not always true , unless ABC is a isosceles triangle ( in this problem it is not ) . Where does that come from ? the bisectors of angles of any triangle will intercept in one point ,O , which is the center of the inscribed circle . its radius r is not necessarily equals the distance between O and A , or B or C . Now , if the triangle is isosceles ,then the altitude and the angle bisector will be the same ( only the one drawn to the third side, not the legs ) you have assumed this case . Hope it is clear .
_________________
Hope this helps Give kudos if it does
Originally posted by foryearss on 03 May 2018, 05:18.
Last edited by foryearss on 03 May 2018, 05:33, edited 1 time in total.



Intern
Joined: 09 Jun 2017
Posts: 49

Re: ABC is a right angled triangle with BC=6cm and AB=8 cm [#permalink]
Show Tags
03 May 2018, 05:30
Quote: ABC is a right angled triangle with BC = 6 cm and AB = 8 cm. AC is hypotenuse. A circle with centre O and radius x has been inscribed. What is the value of x.
A. 2.4 cm B. 2 cm C. 3.6 cm D. 4 cm E. 3 cm I tried to solve it with another method , but had two values for r , why? these triangles are congruent : MOC ,MNC , the area of NOC is r(6r)/2 . the area of MONC is r(6r) these triangles are congruent MOA , AOP , the area of OAP is r(8r)/2 .the area of MOPA is r(8r) the are of the big triangle ABC consists of : MONC , MOPA , and the square shape ONBP which has a side of r . r^2 + r(6r) + r(8r) = 6*8/2 I solved and gor two values for r r=2 r=12 Why am i getting two values one of them is 12 ?
_________________
Hope this helps Give kudos if it does



Manager
Joined: 03 Oct 2016
Posts: 133

Re: ABC is a right angled triangle with BC=6cm and AB=8 cm [#permalink]
Show Tags
03 May 2018, 05:37
005ashok wrote: Attachment: 1796929.png ABC is a right angled triangle with BC = 6 cm and AB = 8 cm. AC is hypotenuse. A circle with centre O and radius x has been inscribed. What is the value of x. A. 2.4 cm B. 2 cm C. 3.6 cm D. 4 cm E. 3 cm As sides BC=6 am and AB = 8 cm, we can derive AC=10 cm. Let BM =h. Area of triangle ABC = \(\frac{1}{2}\)*10*h=\(\frac{1}{2}\)*6*8 > h=4.8 cm. I used simple logic that 2r+something = 4.8 cm so r<2.4 cm . Looking at the answer choices only 2 cm makes sense. Answer: (B).



Manager
Joined: 14 Oct 2017
Posts: 234

Re: ABC is a right angled triangle with BC=6cm and AB=8 cm [#permalink]
Show Tags
09 May 2018, 07:23
stonecold wrote: There are two ways as far as i know i will use the area formula as that is more likely to hit my mind first although the rule states that for any circle to be inscribed in an 90 triangle => the radius => P+B H/2 where P,B,H are three sides of the triangle and H being the largest That is an interesting formula even though you forgot to mark the brackets I think. It should be \(\frac{P+BH}{2}\)  so in this case \(\frac{6+810}{2}= 2\) I will try to remember this formula, thank you!
_________________
My goal: 700 GMAT score
If I could help you with my answer, please think about giving me Kudos



Intern
Joined: 12 Jan 2017
Posts: 10

Re: ABC is a right angled triangle with BC=6cm and AB=8 cm [#permalink]
Show Tags
14 May 2018, 23:50
The easiest way to deal with this question is 6810 is pythagorean triplet. Area of the trinagle = 1/2*6*8 = 24 and also when a circle is inscribed inside a triangle area of the triangle = RS, where R= inradius and S= semiperimeter So, 24= r* (6+8+10)/2 r=2.



Manager
Joined: 22 Feb 2018
Posts: 152

Re: ABC is a right angled triangle with BC=6cm and AB=8 cm [#permalink]
Show Tags
15 May 2018, 01:43
OA: B It is a right angled triangle and 6,8 and 10 are Pythagorean triplet. So AC=10 Radius of Incircle of Right angled triangle is given \(r =\frac{(a+b−c)}{2}\) Where c is hypotenuse, a and b are other two sides. Reason for AE=AD and EC=CF: length of tangents drawn from an external point to a circle are equal here putting c = 10, a=6 , b= 8, we get \(r =\frac{(6+8−10)}{2}=2\) OA=B
_________________
Good, good Let the kudos flow through you



Director
Joined: 02 Oct 2017
Posts: 555

Re: ABC is a right angled triangle with BC=6cm and AB=8 cm [#permalink]
Show Tags
26 May 2018, 08:10
To calculate incentre of right triangle
We have formula
R=( sum of other two sides  hypotenuse)/2
= AB +BCAC/2 =8+610/2= 2
Give kudos if it helps
Posted from my mobile device



Intern
Joined: 27 Nov 2016
Posts: 45
Location: India
GPA: 2.75

Re: ABC is a right angled triangle with BC=6cm and AB=8 cm [#permalink]
Show Tags
28 May 2018, 10:05
005ashok wrote: ABC is a right angled triangle with BC = 6 cm and AB = 8 cm. AC is hypotenuse. A circle with centre O and radius x has been inscribed. What is the value of x. A. 2.4 cm B. 2 cm C. 3.6 cm D. 4 cm E. 3 cm Option B it is. I have a different way of solving it. Please give kudos if it seems interesting to you. Its obvious AC is 10. Now, if a draw a perpendicular from B on AC (Let the length of perpendicular be P), then that line will coincide with the diameter of incircle(with r radius) extended to point B. Now, equate the area of triangle ABC 1/2*AB*BC = 1/2*AC*PFrom this we get P = 4.8 P can also be written as r + r*root2.Hence, when r = 2, then 2 + 2*root2 gives us 2 + 2*1.4 = 2 + 2.8 = 4.8
_________________
Please appreciate with a kudo if my post is helpful to you



Intern
Joined: 30 Nov 2016
Posts: 27

Re: ABC is a right angled triangle with BC=6cm and AB=8 cm [#permalink]
Show Tags
01 Jun 2018, 13:58
This may be a useful shortcut: AP = 8r; And since we know that length of tangents from a single point are equal, hence, AM = 8r Similarly, CM = 6r Also by Pythagoras theorem, AC = 10 So AP + CM = AC => 8r + 6r = 10 Hence r = 2. et voilà
_________________
Good things are going to happen. Keep fighting for what you want. Don't worry and have faith that it'll all work out!



Senior Manager
Joined: 31 Jul 2017
Posts: 368
Location: Malaysia
WE: Consulting (Energy and Utilities)

Re: ABC is a right angled triangle with BC=6cm and AB=8 cm [#permalink]
Show Tags
01 Jun 2018, 23:50
005ashok wrote: ABC is a right angled triangle with BC = 6 cm and AB = 8 cm. AC is hypotenuse. A circle with centre O and radius x has been inscribed. What is the value of x. A. 2.4 cm B. 2 cm C. 3.6 cm D. 4 cm E. 3 cm \(100 = (142r)^2\) \(r = 2cm\)
_________________
If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!



Manager
Joined: 09 Aug 2017
Posts: 96

Re: ABC is a right angled triangle with BC=6cm and AB=8 cm [#permalink]
Show Tags
03 Jun 2018, 05:43
Area = S*r where S=(a+b+c)/3 and r is inner radius. S= 8+6+10/3= 8 A= 24= 1/2*8*6 Hence, r= 2 mm




Re: ABC is a right angled triangle with BC=6cm and AB=8 cm
[#permalink]
03 Jun 2018, 05:43






