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Olympiad workbookIOQMProperties of Triangles

Let A B C be an isosceles triangle with A B=A C and incentre I . If A I=3 and the distance from I to B C is 2 , what is the square of the length of B C ?

Correct answer

80

Step-by-step solution

aligned & I M=r=2 & I A= r A 2 & A 2 = r I A = 2 3 & A 2 = 2 5 = B M A M & 2 5 = a 5 & B C=a=4 5 & B C^2=80 aligned

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