Mathematics
Find the length of the tangent to a circle with radius 5 cm, from a point at a distance of 13 cm from its center.
Circles
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Answer
Consider a circle with center O. Let AP is the tangent of the circle.
We know that,
Tangent and radius to the circle at point of contact are perpendicular to each other.
In the ∆OPA,
∠OAP = 90°.
By pythagoras theorem,
⇒ OA2 + PA2 = OP2
⇒ 52 + PA2 = 132
⇒ 25 + PA2 = 169
⇒ PA2 = 169 - 25
⇒ PA2 = 144
⇒ PA =
⇒ PA = 12 cm
Hence, the length of the tangent = 12 cm.
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