**Two circles intersect at two points B and C. Through B, two line segments ABD and PBQ are drawn to intersect the circles at A, D and P, Q respectively (see figure). Prove that .**

**Solution:**

We need to prove that

** (Angles in the same segment)** ** (1)**

**(Angles in the same segment)** **(2)**

We also have ** (Vertically Opposite Angles)** **(3)**

From **(1), ****(2)** and** (3)**, we get