Mathematics
In the adjoining figure, ABC is a triangle in which AB = AC. P is a point on the side BC such that PM ⊥ AB and PN ⊥ AC. Prove that BM × NP = CN × MP.
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Answer
Consider △ABC
Given, AB = AC
∠ B = ∠ C [Angles opposite to equal sides (Property of isosceles triangle)]
Considering △BMP and △CNP
∠ M = ∠ N = 90°.
∠ B = ∠ C.
So, by AA rule of similarity △BMP ~ △CNP.
As triangles are similar,
Hence proved.
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