geometry olympiad
Geometry
Level
2
In a quadrilateral ABCD, it is given that AB = AD = 13, BC = CD = 20, BD = 24. If r is the radius of the circle inscribable in the quadrilateral, then what is the integer closest to r ? NOTE IF 7.64=8
The answer is 8.
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1 solution
Area of ABCD = Area of ABD + Area of BCD
X= (25 x 12 x 12 x 1)^1/2 + (32 x 8 x 12 x 12)^1/2 = 60 + 192 = 252
Inradius(r) =\frac{area}{semiperimetre}) = 7.64
Hence integer nearest to r is 8