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The bisectors of base angles of a tri...

The bisectors of base angles of a triangle cannot enclose a right angle in any case.

A

yes

B

no

C

cannot determine

D

none of the above

Text Solution

Verified by Experts

The correct Answer is:
B
Given A `DeltaABC` in which BO and CO are the bisectors of the base angles `angleBandangleC` respectively.
PROOF If possible, let `angleBOC=90^(@)`
Then, `angleCBO+angleBCO=180^(@)`
`implies(1)/(2)angleB+(1)/(2)angleC=90^(@)`
`impliesangleB+angleC=180^(@)`
`impliesangleA=0^(@)[:'angleA+angleB+angleC=180^(@)]`
This shows that the points A, B, C do not form a triangle, which is false.
So, our assumption is wrong.
Hence, `angleBOC` is not a right angle.
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