Assertion (A): In the given figure, if O is the centre of the circle, then ∠ACB = 40°.

Reason (R): Angle at the centre is double the angle at the remaining part of the circle.

1. A is true, R is false

2. A is false, R is true

3. Both A and R are true

4. Both A and R are false

From figure,

OA = OB (Radii of same circle)

∠OBA = ∠OAB = 50° (As angles opposite to equal sides in a triangle are equal)

∠OBA + ∠OAB + ∠AOB = 180° [Angle sum property of a triangle]

50° + 50° + ∠AOB = 180°

100° + ∠AOB = 180°'

∠AOB = 180° - 100°

∠AOB = 80°.

We know that,

Angle which an arc subtends at the center is double that which it subtends at any point on the remaining part of the circumference.

So, reason (R) is true.

∠AOB = 2∠ACB

∠ACB = $\dfrac{80°}{2}$ = 40°.

So, Assertion (A) is true.

Both A and R are true.

Hence, option 3 is the correct option.