Olympiad workbookIOQMProperties of Triangles

Triangles ABC and DEF are such that A = D , AB = DE =17, BC = EF =10 and AC - DF =12 . What is AC + DF ?

Correct answer

Step-by-step solution

Let A coincides with D, B coincides with E . With E(B) as centre draw a circle with radius 10 intersecting the line, making angle = A with AB , at F & C . Let N be the foot of perpendicular from B(E) to C F So, BM =8 Hence, AM = 17^2-8^2 = (25)(9) =15 Hence, A F=15-6=9 & A C=15+6=21 So, AC + DF =30

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