Question
From an external point P, two tangents PA and PB are
drawn to a circle with center O. If OP = 13 cm and the radius of the circle is 5 cm, find the length of each tangent.Solution
ATQ,
OP is the distance from center to external point = 13 Radius = 5 OA is perpendicular to PA (radius to the point of tangency). Right triangle OAP: OP2 = OA2 + AP2 132 = 52 + AP2 169 = 25 + AP2 AP2 = 144 AP = 12 cm Length of each tangent = 12 cm.
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