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.

Assertion (A): The line segment joining the mid-points of all parallel chords of a circle passes through the centre.

Reason (R): If the chords are on same side of centre then only the line through the mid-points of the chords passes through the centre.

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 the given figure the lengths of arc AB and arc BC are in the ratio 2:1. If ∠AOB = 96°, then ∠AOC = 144°.

Reason (R): In two equal (congruent) circles if two arcs are equal, then they subtend equal angles at their centres.

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.