Assertion (A): The length of the side of a regular hexagon is equal to the radius of its circumcircle.

Reason (R):

∠AOB = $\dfrac{360°}{6} = 60°$
∠OAB = ∠OBA = $\dfrac{180° - 60°}{2} = 60°$
⇒ OAB is an equilateral triangle
So, AB = OA = radius (r) of the circumcircle

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.

Assertion (A): Rhombus becomes square if its diagonals are equal.

Reason (R): OB = OD = $\dfrac{1}{2}\times \text{BD}$

and OC = OA = $\dfrac{1}{2}\times \text{AC}$
⇒ OB = OA = OC
OB = OC
⇒ ∠a = ∠b = 45°
Similarly, ∠c = ∠d = 45°
∠ABC = ∠b + ∠c = 45° + 45° = 90°

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.

Assertion (A): In △ABC, BD : DC = 1 : 2 and OA = OD

Area of △AOB : area of △ABC = 1 : 4

Reason (R):

Area of △AOB = $\dfrac{1}{2}\times \text{area of △ABD}$
=$\dfrac{1}{2}\times \dfrac{2}{3}\times \text{area of △ABC}$

=$\dfrac{1}{3}\times \text{area of △ABC}$

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.

Assertion (A): AM and BN are tangents to the same circle at points A and B respectively. Then AN = BM.

Reason (R): Since, tangents to a circle are equal in length

⇒ AM = BN

△APN ≅ △BPM ⇒ AN = BM

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.