Multiple choice

If two tangents inclined at an angle $60^0$ are drawn to a circle of radius 3 cm. The distance of the chord joining the point of contact of the tangents to the circle is $ 1.5cm. $ Then length of each tangent is equal to

  1. $\frac{3}{2}\sqrt{3}$ cm

  2. 6 cm

  3. 3 cm
  4. $3\sqrt{3}$ cm
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the tangents be PA and PB. In the triangle formed by the center O, the point of contact A, and the external point P, we have a right triangle OAP. Angle OPA = 30 degrees (half of 60). tan(30) = OA / AP = 3 / AP. AP = 3 / tan(30) = 3 / (1/sqrt(3)) = 3 * sqrt(3).

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