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Question
The bisectors of base angles of a triangle cannot enclose a right angle in any case.
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Solution
In a ABC
Sum of all angles of triangles is `180^@`
i.e, `∠ A+∠ B+∠C =180^@` divide both sides by `2`
⇒ `1/2∠A+1/2∠B+1/2∠C=180^@`
⇒`1/2∠A+∠OBC+∠OBC=90^@` [∵ OB,OC insects ∠B and ∠C]
⇒`∠OBC+∠OCB=90^@-1/2A`
Now in `Δ OCB=180^@`
`∴ ∠ BOC+∠OBC+∠OCB=180^@`
⇒`∠ BOC+90^@-1/2∠A=180^@`
⇒ `∠ BOC=90^@-1/2 ∠A`
Hence, bisectors of a base angle cannot enclose right angle.
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