In the following figure, PQ is the common tangent to both the circles. SR and PT are tangents. If SR=4 cm,PT=7 cm, then find RP.

In the following figure, $PQ$ is the common tangent to both the circles. SR and PT are tangents. If $SR = 4 cm, PT = 7 cm,$ then find RP.

A
1cm
B
2cm
C
3cm
D
4cm

Solution:

Given is a figure,

SR = 4 cm, PT = 7 cm,

Tangent from the same points to a circle is equal in length,
QR = RS and PQ = PT.
Therefore,

Q R = R S = 4 cm

and

P Q = P T = 7 cm

.

P Q = Q R + P R ⇒ P R = P Q − Q R ⇒ P R = 7 − 4 ⇒ P R = 3 cm

Thus, the required length is PR = 3 cm.
Therefore, option (3) is correct.

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