Given:
Angle A is circumscribed about circle O.
m∠CDB = 48°
To find:
The measure of angle A.
Solution:
OC and OB are radius of circle O.
AC and AB are tangents of circle O.
The angle between tangent and radius is always 90°.
⇒ m∠OCA = 90° and m∠OBA = 90°
The angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.
⇒ m∠COB = 2 × m∠CDB
⇒ m∠COB = 2 × 48°
⇒ m∠COB = 96°
Sum of all the angles of quadrilateral is 360°.
m∠BAC + m∠OCA + m∠COB + m∠OBA = 360°
m∠BAC + 90° + 96° + 90° = 360°
m∠BAC + 276° = 360°
Subtract 276° from both sides.
m∠BAC = 84°
The measure of ∠A is 84°.
