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From an external point two tangents to a circle are drawn. The chord passing through the points of contact subtends an angle 72° at the centre. The angle between the tangents is
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- 36°
- 72°
- 108°
- 144°
- 36°
Correct Option: C
As per the given in question , we draw a figure of circle in which two tangents are drawn from an external point
From figure , OA = OB = radii of circle
Given , ∠AOB = 72°;
∠OBP = ∠OAP = 90°
In ∠OAB,
∠OAB = ∠OBA
∴ 2 ∠OAB = 180° – 72° = 108°
| ⇒ ∠OAB = | = 54° | |
| 2 |
∴ ∠PBA = ∠PAB = 90° – 54° = 36°
∴ ∠BPA = 180° – 2 × 36°
∠BPA = 180° – 72° = 108°
