Mathematics — CBSE Class 10 board question

Let the external point be P and centre be O. The angle between the two tangents = 60°, so ∠TPO = 30° (since OP bisects the angle between tangents).

Radius OT = 3 cm, ∠OTP = 90° (radius ⊥ tangent).

In right △OTP:

$$\tan 30° = \frac{OT}{TP} \Rightarrow \frac{1}{\sqrt{3}} = \frac{3}{TP}$$

$$TP = 3\sqrt{3} \text{ cm}$$

The length of each tangent is $3\sqrt{3}$ cm.

Source: Chapter 10, Circles

---

• The key property used: radius is perpendicular to tangent at point of contact (Theorem 10.1), and OP bisects the angle between the two tangents (since the two tangents from an external point are equal).
• The full angle between tangents is 60°, so the half-angle at P in the right triangle is 30°. Use tan 30° = opposite/adjacent = radius/tangent length.
• Examiners expect you to show the right triangle formation and the trigonometric step clearly.