Property of isosceles triangles

Geometry Level 3

In an isosceles triangle $ABC$ , $AB=AC$ , $P$ is any point on $BC$ , $PR$ is perpendicular to $AB$ , and $PY$ is perpendicular to $AC$ .

If the length of altitude $BM$ is 17, find $PR+PY$ .

The answer is 17.

1 solution

Aparna Phadke
Jan 6, 2019

If we connect AP, and formulate area of ABC in two ways, we get, PR X AB/2 + PY X AC/2 = BM X AC/2. Since AB = AC, (PR X AC + PY X AC)/2 = BM X AC/2. Therefore, AC X ( PR + PY)/2 = BM X AC/2 Multiplying 2/AC on both sides, we get, PR + PY = BM. BM being 17, PR + PY = 17.

Property of isosceles triangles

The answer is 17.

1 solution

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