In the given circle, ∠BAD = 95°, ∠ABD = 40° and ∠BDC = 45°.

Assertion (A) : To show that AC is a diameter, the angle ADC or angle ABC need to be proved to be 90°.

Reason (R) : In △ADB,

∠ADB = 180° - 95° - 40° = 45°

∴ Angle ADC = 45° + 45° = 90°

(i) A is true, R is false

(ii) A is false, R is true

(iii) Both A and R are true and R is correct reason for A

(iv) Both A and R are true and R is incorrect reason for A

ABCD is a cyclic quadrilateral, BD and AC are its diameters. Also, ∠DBC = 50°.

Assertion (A) : ∠BAC = 40°.

Reason (R) : ∠BAC = ∠BDC = 180° - (50° + 90°) = 40°.

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true and R is correct reason for A.

4. Both A and R are true and R is incorrect reason for A.

AB is diameter of the circle and ∠ACD = 38°.

Assertion (A) : x = 38°.

Reason (R) : ∠ACB = 90°, x = ∠DCB = 90° - 38° = 52°.

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true and R is correct reason for A.

4. Both A and R are true and R is incorrect reason for A.

Chords AC and BD intersect each other at point P.

Assertion (A) : PA x PC = PB x PD.

Reason (R) : Δ APD ∼ Δ BPC

$\Rightarrow \dfrac{PA}{PB} = \dfrac{PD}{PC}$

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true and R is correct reason for A.

4. Both A and R are true and R is incorrect reason for A.