In Fig. 16.193, two circles intersect at A and B. The centre of the smaller circle is O and it lies on the circumference of the larger circle. If ∠APB=70°, find ∠ACB.

Prove that the line segment joining the mid-point of the hypotenuse of a right triangle to its opposite vertex is half of the hypotenuse.

In Fig. 16.189, ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If ∠DBC=55° and ∠BAC=45°, find ∠BCD.

In Fig. 16.194, two congruent circles with centres O and O’ intersect at A and B. If ∠AO’B=50°, then find ∠APB.

In Fig. 16.195, ABCD is a cyclic quadrilateral in which ∠BAD=75°, ∠ABD=58° and ∠ADC=77°, AC and BD intersect at P. Then, find ∠DPC.