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Olympiad workbookIOQMProperties of Triangles

In a quadrilateral A B C D , it is given that A B=A D=13, B C=C D=20, B D=24 . If r is the radius of the circle inscribable in the quadrilateral, then what is the integer closest to r ?

Correct answer

8

Step-by-step solution

aligned Area of A B C D & = Area of A B D+ Area of B C D & = 25 12 12 1 + 32 8 12 12 & =60+192=252 Inradius(r) & = Area semi-perimeter = 252 33 = 84 11 =7 . 64 aligned Hence integer nearest to r is 8.

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