From an outside point P, two tangents, PA and PB, are drawn to a circle. Given that the length of PA is 12 cm, what is the length…

Question

From an outside point P, two tangents, PA and PB, are drawn to a circle. Given that the length of PA is 12 cm, what is the length of PB?

1. A. 6 cm
2. B. 10 cm
3. C. 12 cm (Correct answer)
4. D. 24 cm

Correct Answer

Option C — 12 cm

Detailed Solution & Explanation

The correct answer is 12 cm.

Key Points

• Two tangents drawn to a circle from the same external point are always equal in length.
• Since PA and PB are both tangents from P, PB = PA = 12 cm.
• This 'equal tangents from an external point' theorem is a one-line result — no radius, centre or right-angle construction is needed once you recognise both segments are tangents from the same point.