CBSE Class 9 Answered

common tangents are drawn from poin P to circle that meet the circle at A and B.

From center of circle line OP is drawn . A and B are connected to center O of circle by line as shown in figure.

Δ PBO and Δ PAO are right triangles because OA and OB are prependiculars to tangents.

Hence OP is common hypotenuse of both right triangles .since OA = OB ( radii of circle) ,  Δ PBO and Δ PAO are congruent .

Hence APO = BPO = 25^o

POB = 90^o - BPO = 90^o - 25^o = 65^o .