right triangle in the circle

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ket: Senior | Next Rank: 100 Posts; Posts: 93; Joined: Sun Mar 15, 2009 9:07 am; Thanked: 7 times

by ket » Wed Nov 25, 2009 1:32 am

I have this question, if you have answer then please respond.

I know that if the triangle is inscribed in the circle and has diameter as one of its side than it is a right triangle, but is the reversed also true?

I mean if problem says that right triangle is inscribed in the circle, does it mean that hypotenuse of the triangle is definately diameter?

Thanks.

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Source: Beat The GMAT — Problem Solving | Wed Nov 25, 2009 1:32 am

papgust: Community Manager; Posts: 1537; Joined: Mon Aug 10, 2009 6:10 pmFollowed by: 252 members; Thanked: 653 times

by papgust » Wed Nov 25, 2009 1:36 am

ket wrote:I have this question, if you have answer then please respond.

I know that if the triangle is inscribed in the circle and has diameter as one of its side than it is a right triangle, but is the reversed also true?

I mean if problem says that right triangle is inscribed in the circle, does it mean that hypotenuse of the triangle is definately diameter?

Thanks.

Yes, the hypotenuse of the triangle is definitely a diameter.

Because, there is a rule in geometry - "An Angle formed inside a semi-circle is always a right-angle". Hypotenuse is the side opp to 90 degrees, which is nothing but the diameter of a circle.

Hope it is clear now.

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