Mathematics
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
- A is true, R is false.
- A is false, R is true.
- Both A and R are true.
- Both A and R are false.
Circles
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Answer
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.
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