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In ∆ABC, ∠A = 90°, BP and CQ are two medians. Then the value of BP² + CQ² BC²
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4 5 -
5 4 -
3 4 -
3 5
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Correct Option: B
On the basis of given in question , we draw a figure triangle ABC ,
In ∆ AQC,
∠A = 90°
⇒ CQ² = AC² + QA²
⇒ 4CQ² = 4AC² + 4QA²
⇒ 4CQ² = 4AC² + (2QA)²
⇒ 4CQ² = 4AC² + AB²
[∵AB = 2QA]
In ∆ BPA,
BP² = BA² + AP²
⇒ 4BP² = 4BA² + 4AP²
⇒ 4BP² = 4BA² + AC²
[∵ AC = 2AP]
∴ 4 CQ² + 4 BP² = 4 AC² + AB² + 4 AB² + AC²
⇒ 4(CQ² + BP²) = 5(AC² + AB²) = 5 BC²
| ⇒ | = | ||
| BC² | 4 |
