1) AB and CB are two chords of circle. Prove that BO bisects angle 8. (3)
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Step-by-step explanation:
Given: In the figure, AB = CB and O is the centre of the circle.
To Prove: BO bisects ∠ABC.
Construction: Join OA and OC.
Proof : In ∆OAB and ∆OCB,
OA = OC [Radii of the same circle]
AB = CB [Given]
OB = OB [Common]
∴ ∆OAB ≅ ∆OCB [By SSS]
∴ ∠ABO = ∠CBO [By cpctc]
⇒ BO bisects ∠ABC.
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