Bisect it

Geometry Level pending

In Δ A B C \Delta ABC , angle bisector of ∠ A B C \angle ABC meets A C AC at point D D . If B C = 6 , A C = 40 , C D = 15 BC = 6 \ , \ AC = 40 \ , \ CD = 15 then find A B AB .


The answer is 10.

Gean Llego by Gean Llego , 25, Philippines

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1 solution

By angle bisector theorem, AB's length is easily obtained to be 4. However, if AB=10, triangle inequality is violated, hence this question is actually flawed.

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Well apparently, if we use proportion to triangle similarity we will get; 6 : 15 = AB : 25 -- and therefore AB is 10. The question is not flawed.

Gean Llego - 5 years, 5 months ago

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I meant that the triangle stated in the question is actually impossible to construct, as it has sides 10, 6 and 40.

A Former Brilliant Member - 5 years, 5 months ago

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Well dreary, this question is in fact in the MCC. And with that, I just realized it tho. HAHAHA

Gean Llego - 5 years, 5 months ago

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