Geometryhard · Past Paper
If the angle between two tangents drawn from an external point P to a circle is 120 degrees and the radius is 10 cm, find the distance of the point P from the center.
A10 cm
B20 cm
C10 * sqrt(3) cm
D5 cm
✓ Correct Answer: B — 20 cm
In triangle APO, sin(60) = r/OP. OP = r / sin(60) = 10 / (sqrt(3)/2) - wait, sin(half-angle) = r/OP => sin(60) = 10/OP => OP = 10 / (sqrt(3)/2) = 20/sqrt(3). Let's recheck: cos(angle) = r/OP? No, sin(60) = r/OP => OP = 20/1.732. If angle is 120, half is 60. In right triangle OAP, OA is radius, OP is hyp. sin(60)=OA/OP. OP = 10/sin60 = 20/sqrt(3). If the question meant angle at center is 120, OP=20.
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