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In the given 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 x NP = CN x MP.
In the given 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 x NP = CN x MP.
CBSE | Class 10 | Maths | ML Aggarwal | Similarity
In the given 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 x NP = CN x MP.

Solution:-

From the question it is given that, ABC is a triangle in which AB = AC.

P is a point on the side BC such that PM ⊥ AB and PN ⊥ AC.

We have to prove that, BM x NP = CN x MP

Consider the ∆ABC

AB = AC … [from the question]

∠B = ∠C … [angles opposite to equal sides]

Then, consider ∆BMP and ∆CNP

∠M = ∠N

Therefore, ∆BMP ~ ∆CNP

So, BM/CN = MP/NP

By cross multiplication we get,

BM x NP = CN x MP

Hence it is proved.

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