Property of isosceles triangle

Geometry Level 2

In an isosceles triangle ABC, P is any point on BC. PR is perpendicular to AB, PY IS perpendicular to AC. If the length of altitude BM is 17 find (PR+PY).


The answer is 17.

Aparna Phadke by Aparna Phadke , 16, India

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1 solution

Sumant Chopde
Jan 14, 2019

Assuming A B = A C AB=AC , If we are allowed to take point P P on side B C BC , why not take P P on the point B B ? Then P Y = B C PY = BC and P R = 0 PR = 0 . Hence, P Y + P R = 0 + 17 = 17 PY + PR = 0 +17=17 .

0 Helpful 0 Interesting 0 Brilliant 0 Confused

this problem is badly stated : we don't know if the triangle is isosceles because AB=AC or AB=BC. In all cases, PY+PR also depends on the length of the third side, so it is impossible to answer. The proposed answer is not correct because if P in on B, PY is not BC (PY is perpendicular to AC, and angle C cannot be 90°).

Gerard Boileau - 2 years, 4 months ago

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