1) If on a plane \(AB = BC = CA = DA\), then find:
(a) Angle BDC if \( \angle BDC < 90^\circ \)
(b) Angle BDC if \( \angle BDC > 90^\circ \)

2) If A is the centre of a circle and B, C and D lie on the circle such that ABCD is a rhombus, find:
(a) Angle BAD?
(b) If radius is 8 cm then find the area of that rhombus.

3) Points A, B, C and D are on a circle. Line AB and DC are extended to meet at P (outside the circle), and lines BC and AD are extended to meet at Q. Find angle ∠PCQ if ∠APD = 30° and ∠AQB = 40°.

4) Same setup as above. Find angle ∠BCD if ∠APD = 40° and ∠AQB = 50°.

5) Same setup as above. Find angle ∠ABC if ∠APD = 45° and ∠AQB = 25°.

6) Same setup as above. Find angle ∠ADC if ∠APD = 15° and ∠AQB = 65°.

7) Same setup as above. Find angle ∠APD if ∠PCQ = 125° and ∠AQB = 35°.

8) Two chords AB and CD of a circle intersect inside the circle at point O. Arcs AC and DB subtend angles 70° and 50° at the center. Find angle ∠AOC.

9) Same setup. Arcs AC and DB subtend angles 30° and 80° respectively. Find angle ∠DOB.

10) Two chords AB and CD are extended to meet at point P outside the circle. Arcs AC and DB subtend angles 140° and 80° at the center. Find angle ∠APC.

11) Two chords AB and CD are extended to meet at point P outside the circle. Arcs AC and DB subtend angles 124° and 74° at the center. Find angle ∠AQC if Q is the midpoint of arc AC.

12) Two chords AB and CD are extended to meet at point P outside the circle. Arc AC subtends 60° at the perimeter. If angle ∠BQD = 140° where Q is a point on arc BD, find angle ∠APD.