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If P and Q are the mid points of the sides CA and GB respectively of a triangle ABC, right-angled at C. Then the value of 4 (AQ2 + BP2) is equal to :
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- 4 BC2
- 5 AB2
- 2 AC2
- 2 BC2
- None of these
Correct Option: B
From given figure , we have
AQ2 = AC2 + QC2
BP2 = BC2 + CP2
AQ2 + BP2 = (AC2 + BC2) + (QC2 + CP2) = AB2 + PQ2.
| ∴ AQ2 + BP2 = AB2 + |  | 1 | AB |  | × | | 1 | AB | |  | ∵ PQ = | 1 | AB |  |
| 2 | 2 | 2 |
| AQ2 + BP2 = | 5 | AB2 ⇒ 4(AQ2 + BP2) = 5AB2 |
| 4 |
