Q. 29

In a right triangle ABC right-angled at B, if P and Q are points on the sides AB and AC respectively, then
A. AQ2 + CP2 = 2 (AC2+ PQ2)

B. 2 (AQ2 + CP2) = AC2 + PQ2

C. AQ2 + CP2 = AC2 + PQ2

D. AQ + CP=(AC + PQ).

Answer :

Given in right triangle ABC right-angled at B, P and Q are points on the sides AB and BC respectively.



Applying Pythagoras Theorem,


In ΔAQB,


AQ2 = AB2 + BQ2 … (1)


In ΔPBC,


CP2 = PB2 + BC2 … (2)


Adding (1) and (2),


AQ2 + CP2 = AB2 + BQ2 + PB2 + BC2 … (3)


In ΔABC,


AC2 = AB2 + BC2 … (4)


In ΔPBQ,


QP2 = PB2 + BQ2 … (5)


From (3), (4) and (5),


AQ2 + CP2 = AC2 + PQ2

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