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Question

State whether following statement is true or false.
The external bisector of an angle of a triangle divides the opposite side externally in the ratio of the sides containing the angle.

A
True
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B
False
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Solution

The correct option is A True
In ABC,AD is the external bisector of BAC and intersects BC produced at D

Draw CEDA meeting AB at E

CEDA and AC is the transversal.

ECA=CAD ....(1) alternating angles
Also CEDA and BP is a transversal.

CEA=DAP.....(2) corresponding angles.

But AD is the bisector of CAP

CAD=DAP .........(3)

From (1),(2) and (3) we have

CEA=ECA(sides opposite to equal angles are equal)
In BDA, we have ECAD

BDDC=BAAE(by thales theorem)

BDDC=BAAC since AE=AC

Hence proved.

1495734_177267_ans_00aa3f18b6c74c37932afec6850beb2f.png

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