GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 22 Mar 2019, 09:34

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# A triangle is inscribed in a circle. A point is randomly chosen inside

Author Message
TAGS:

### Hide Tags

Manager
Joined: 30 Dec 2016
Posts: 235
GMAT 1: 650 Q42 V37
GPA: 4
A triangle is inscribed in a circle. A point is randomly chosen inside  [#permalink]

### Show Tags

12 Feb 2018, 08:20
1
4
00:00

Difficulty:

85% (hard)

Question Stats:

39% (01:43) correct 61% (01:35) wrong based on 83 sessions

### HideShow timer Statistics

A triangle is inscribed in a circle. A point is randomly chosen inside the circle. What is the probability that point lies on the area common to triangle and circle?

A) Longest side of triangle ABC measures 10.

B) ABC is a right isosceles triangle.

Source: Experts Global

_________________

Regards
SandySilva

____________
Please appreciate the efforts by pressing +1 KUDOS (:

Math Expert
Joined: 02 Aug 2009
Posts: 7431
A triangle is inscribed in a circle. A point is randomly chosen inside  [#permalink]

### Show Tags

12 Feb 2018, 08:45
3
1
sandysilva wrote:
A triangle is inscribed in a circle. A point is randomly chosen inside the circle. What is the probability that point lies on the area common to triangle and circle?

A) Longest side of triangle ABC measures 10.

B) ABC is a right isosceles triangle.

Source: Experts Global

Since we are looking at probability, even finding ratio of areas will be sufficient...

Statement I does not say anything about radius of circle or area of triangle..
Insufficient

Statement II states ABC is isosceles right angle triangle....
Remember the rule - any angle in the semicircle with two sides meeting the end of diameter is 90..
So here the Dia of circle is hypotenuse of triangle...
Since triangle is isosceles, sides of triangle and radius are related..
We can find the ratio of two areas..
Sufficient
. B

Otherwise..
Sides of isosceles right angle triangle = Dia/√2 = 2r/√2=√2r
Area of isosceles triangle =$$\frac{1}{2}*√2r*√2r=r^2..$$
Area of circle=$$π*r^2$$..
Probability = $$\frac{r^2}{π*r^2}=\frac{1}{π}$$
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

GMAT Expert

Senior Manager
Joined: 15 Oct 2017
Posts: 308
GMAT 1: 560 Q42 V25
GMAT 2: 570 Q43 V27
GMAT 3: 710 Q49 V39
Re: A triangle is inscribed in a circle. A point is randomly chosen inside  [#permalink]

### Show Tags

12 Feb 2018, 09:04
B.

A) No information about triangle's type (scalene or isosceles) and radius or diameter of the circle. Not Sufficient.
B) Right isosceles triangle means diameter is the hypotenuse and is equal to 2r.
Area of triangle = 1/2*2r*r = r^2
Area of circle = 22/7*r^2
Therefore probability = r^2/(22/7*r^2) = 7/22 = Sufficient.
Intern
Joined: 15 Oct 2016
Posts: 29
Re: A triangle is inscribed in a circle. A point is randomly chosen inside  [#permalink]

### Show Tags

12 Feb 2018, 20:38
sandysilva wrote:
A triangle is inscribed in a circle. A point is randomly chosen inside the circle. What is the probability that point lies on the area common to triangle and circle?

A) Longest side of triangle ABC measures 10.

B) ABC is a right isosceles triangle.

Source: Experts Global

We don't need to do calculations to solve this one!

If you know that it is a right isosceles triangle, then the longest side must be the diameter and the relative orientation and relative length of other sides are known. Therefore, we would also know the ratio of areas of the triangle to the circle. Hence statement B alone is sufficient.
Non-Human User
Joined: 09 Sep 2013
Posts: 10177
Re: A triangle is inscribed in a circle. A point is randomly chosen inside  [#permalink]

### Show Tags

15 Feb 2019, 02:59
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: A triangle is inscribed in a circle. A point is randomly chosen inside   [#permalink] 15 Feb 2019, 02:59
Display posts from previous: Sort by