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 ______.

पर्याय

• 4.2 cm

• 2.1 cm

• 8.4 cm

• 6.3 cm

Answer 1

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 8.4 cm.

Explanation:

The figure shows two circles touching externally at point A, with QR being a common tangent. The tangent at A meets QR at point P, and we are given that the length AP = 4.2 cm. To find the length of QR, we can use the fact that the tangents drawn from an external point to a circle are equal in length.

Since A is the point of tangency for both circles, the lengths of the tangents from P to each point of tangency (which are Q and R respectively) will be equal. Thus, PQ = PR = AP.

Given AP = 4.2 cm, we can say PQ = PR = 4.2 cm.

Therefore, the length of QR,

QR = PQ + PR 

QR = 4.2 + 4.2 

QR = 8.4 cm