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Question
In the given figure AC is a tangent to the circle with centre O.
If ∠ADB = 55° , find x and y. Give reasons for your answers.
Solution
In ΔABD, ∠BAD = 90°
∴ ∠ABD + ∠BAD + ∠ADB = 180° {Sum of angles in a triangle}
∴ ∠ABD + 90° + 55° =180°
∴ ∠ABD = 35°
Also ∠AOE = 2∠ABE = 2∠ABD
∴ ∠AOE = y = 2 × 35°
| y = 70° |
In Δ AOC,
∠OAC + x + y = 180°
∴ 90° + x + 70° = 180°
∴ 90° + x + 70° = 180°
| ⇒ x = 20° |
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