In figure, AB = CB and O is the centre of the circle. Prove that BO bisects $∠$ ABC

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Solution

To prove : BO bisects $∠$ ABC

Construction :Join OA and OC.

Proof : In $Δ$ OAB and $Δ$ OCB

Statement Reason

OA = OC [Radii of the same circle]

AB = CB [Given]

OB = OB [Common]

$∴ Δ O A B ≅ Δ O C B$ [By SSS]

$∠$ ABO = $∠$ CBO [C.P.C.T]

$∴$ BO bisects $∠$ ABC

Hence proved

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Similar questions

In figure AB = CB and O is the centre of the circle. Prove that BO bisects $∠ A B C$ . [1 MARK]

In the figure, O is the centre of the circle, BO is the bisector of $∠ A B C$ . Show that AB = BC.

△ A E O \sim △ A B C .

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