Tangents and Intersecting Chords

Two circles with centres O and O’ are drawn to intersect each other at points A and B. Centre O of one circle lies on the circumference of the other circle and CD is drawn tangent to the circle with centre O’ at A. Prove that OA bisects angle BAC.

Solution: Join \[OA,\text{ }OB,\text{ }OA,\text{ }OB\text{ }and\text{ }OO\] \[CD\]is the tangent and \[AO\]is the chord. \[\angle OAC\text{ }=\angle OBA\text{ }\ldots \text{ }\left( i \right)\] ...

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