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ABC is a right angled triangle with BC=6cm and AB=8 cm
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18 Jan 2014, 06:52
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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:
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Re: ABC is a right angled triangle with BC=6cm and AB=8 cm
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19 Jan 2014, 17:24
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




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Re: ABC is a right angled triangle with BC=6cm and AB=8 cm
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19 Jan 2014, 14:28
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
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Re: ABC is a right angled triangle with BC=6cm and AB=8 cm
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06 Jul 2015, 07:12
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
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Re: ABC is a right angled triangle with BC=6cm and AB=8 cm
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06 Jul 2015, 09:39
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
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Re: ABC is a right angled triangle with BC=6cm and AB=8 cm
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27 Dec 2015, 09:22
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.



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Re: ABC is a right angled triangle with BC=6cm and AB=8 cm
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03 Apr 2016, 21:06
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
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Re: ABC is a right angled triangle with BC=6cm and AB=8 cm
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Updated on: 03 May 2018, 04:33
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 .
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Originally posted by foryearss on 03 May 2018, 04:18.
Last edited by foryearss on 03 May 2018, 04:33, edited 1 time in total.



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Re: ABC is a right angled triangle with BC=6cm and AB=8 cm
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03 May 2018, 04:30
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 ?
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Re: ABC is a right angled triangle with BC=6cm and AB=8 cm
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03 May 2018, 04:37
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).
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Re: ABC is a right angled triangle with BC=6cm and AB=8 cm
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09 May 2018, 06:23
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!
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Re: ABC is a right angled triangle with BC=6cm and AB=8 cm
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14 May 2018, 22:50
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.



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Re: ABC is a right angled triangle with BC=6cm and AB=8 cm
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15 May 2018, 00:43
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
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Re: ABC is a right angled triangle with BC=6cm and AB=8 cm
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26 May 2018, 07:10
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
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Re: ABC is a right angled triangle with BC=6cm and AB=8 cm
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28 May 2018, 09:05
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
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Re: ABC is a right angled triangle with BC=6cm and AB=8 cm
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01 Jun 2018, 12:58
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
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Re: ABC is a right angled triangle with BC=6cm and AB=8 cm
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01 Jun 2018, 22:50
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 \(100 = (142r)^2\) \(r = 2cm\)
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Re: ABC is a right angled triangle with BC=6cm and AB=8 cm
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03 Jun 2018, 04:43
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



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Re: ABC is a right angled triangle with BC=6cm and AB=8 cm
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12 Sep 2018, 09:15
Quick elimination tip BC = 6 BC > BM BM > 2r Therefore 3 > r Eliminate C, D, E, guess and move on.
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