Mathematics
O is the center of a circle with diameter 30 cm. P is a point outside the circle and PA is tangent of the circle. Find :
(i) the length of tangent PA; if OP = 39 cm.
(ii) the distance between O and P, if the length of the tangent PA is 20 cm.
Circles
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Answer
Given, diameter = 30 cm
As we know that the diameter is twice the radius.
⇒ Radius = = 15 cm.
(i) It is given that OP = 39 cm.
In ∆ OPA,
∠OAP = 90°.
By pythagoras theorem,
⇒ OA2 + PA2 = OP2
⇒ 152 + PA2 = 392
⇒ 225 + PA2 = 1521
⇒ PA2 = 1521 - 225
⇒ PA2 = 1296
⇒ PA =
⇒ PA = 36 cm.
Hence, the length of tangent PA = 36 cm.
(ii) Given,
PA = 20 cm
⇒ OA2 + PA2 = OP2
⇒ 152 + 202 = OP2
⇒ 225 + 400 = OP2
⇒ OP2 = 625
⇒ OP =
⇒ OP = 25 cm.
Hence, the distance between O and P = 25 cm.
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