#### (a) In the figure (i) given below, APC, AQB, and BPD are straight lines.

(i) Prove that ∠ADB + ∠ACB = 180°.

(ii) If a circle can be drawn through A, B, C, and D, Prove that it has AB as a diameter

#### (b) In the figure (ii) given below, AQB is a straight line. Sides AC and BC of ∆ABC cut the circles at E and D respectively. Prove that the points C, E, P, and D are concyclic.

**Solution:**

**More Solutions:**

- Draw an equilateral triangle of side 5 cm and draw its inscribed circle.
- Triangle ABC with BC = 6.4 cm, CA = 5.8 cm and ∠ ABC = 60°
- Construct a triangle ABC in which BC = 4 cm, ∠ACB = 45°.
- Construct a circle circumscribing the hexagon.
- Draw a circle of radius 3 cm. Mark its centre as C
- Construct a triangle ABC having given c = 6 cm, b = 1 cm and ∠A = 30°.