#### Question

Two circle 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, OB, O'A, O'B and O'O.

CD is the tangent and AO is the chord.

`∠`OAC = `∠`OBA (angles in alternate segment)

In ΔOAB ,

OA = OB (Radii of the same circle)

∴ OAB = `∠`OBA …..(ii)

From (i) and (ii)

`∠`OAC = `∠`OAB

Therefore, OA is bisector of `∠`BAC

Is there an error in this question or solution?

Solution Two Circle with Centres O and O ' Are Drawn to Intersect Each Other at Points a and B.Prove that Oa Bisects Angle Bac. Concept: Tangent Properties - If Two Circles Touch, the Point of Contact Lies on the Straight Line Joining Their Centers.