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.

Both A and R are false.

Explanation

The theorem states that two tangents drawn to a circle from the same external point are equal in length.

However, the Assertion (A) mentions that AM and BN are tangents drawn to the circle from two different points A and B, respectively.

Hence, the theorem is not applicable to this case.

∴ Assertion (A) is false.

The Reason (R) mentions that tangents to a circle are equal in length.

However, as per the theorem, the two tangents should be drawn from the same external point to be equal in length.

∴ Reason (R) is false.

Hence, both Assertion (A) and Reason (R) are false.