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In the given figure, D is the midpoint of side BC and AE⊥BC. If BC = a, AC = b, AB = c, AD = p and AE = h, prove that

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In the given figure, D is the midpoint of side BC and AE⊥BC. If BC = a, AC = b, AB = c, AD = p and AE = h, prove that 

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(i) In right-angled triangle AEC, applying Pythagoras theorem, we have:

(ii) In right-angled triangle AEB, applying Pythagoras, we have:

(iii) Adding (i) and (ii), we get:

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