In the given figure, $QR$ is a common tangent to the two given circles touching externally at $A$. The tangen…

Question

In the given figure, $QR$ is a common tangent to the two given circles touching externally at $A$. The tangent at $A$ meets $QR$ at $P$. If $AP = 4.2$ cm, then the length of $QR$ is :

Accepted Answer

## Model Answer **(C) 8.4 cm** By the equal tangent theorem, from external point P: PQ = PA = 4.2 cm and PR = PA = 4.2 cm. Therefore, QR = PQ + PR = 4.2 + 4.2 = **8.4 cm**. Source: Chapter 10, Theorem 10.2 ## Explanation P is an external point to both circles. Tangents from P to the first circle: PA = PQ (equal tangents). Tangents from P to the second circle: PA = PR (equal tangents). So QR = QP + PR = 2 × 4.2 = 8.4 cm. Examiners expect you to cite the equal-tangents theorem.

Mathematics — CBSE Class 10 board question