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 true, R is true

(iii) A is false, R is false

(iv) A is false, R is true

We know that,

Angle in semicircle is a right angle.

If AC is the diameter, then ∠ADC = ∠ABC = 90°.

∴ Assertion (A) is true.

From figure,

In △ADB,

By angle sum property of triangle,

∴ ∠ADB + ∠DBA + ∠BAD = 180°

⇒ ∠ADB + 40° + 95° = 180°

⇒ ∠ADB + 135° = 180°

⇒ ∠ADB = 180° - 135° = 45°.

From figure,

⇒ ∠ADC = ∠ADB + ∠BDC = 45° + 45° = 90°.

∴ Reason (R) is true.

Hence, Option 2 is the correct option.