Triangle Problem

Geometry Level 3

In triangle $ABC$ , we are given $\angle ABC = \angle BCA \ne \angle CAB$ . If $n$ and $m$ denote the largest and smallest possible values of $\angle CAB$ , find $\frac{n + m}{2}$ .

90 63 91 75

1 solution

Edwin Gray
Sep 23, 2018

Let <ABC = <BCA = t. Then <BAC = 180 - 2t. We cannot assume that the angles are integers, even though the problem is somewhat phrased with that expectation. Therefore the largest angle , m, is as close to 180 as you want, whereas the smallest value, n , is as close to 0 as you wish. No matter what you choose, the average will be 90. Ed Gray

Triangle Problem

1 solution

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