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प्रश्न
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 ______.
विकल्प
4.2 cm
2.1 cm
8.4 cm
6.3 cm
उत्तर
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
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