AB is a chord in a circle with centre O. AB is produced to C such that BC is equal to the radius of the circle. C is joined to O and produced to meet the circle at D. of ∠ACD = 32°, then the measure of ∠AOD is ........
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 96°
| Understanding | Application |
| Tricks |  |
| Now |
In ΔOBC OB = BC given ∴ ∠BOC = 32 = ∠BCO So ∠ABO = ∠BOC + ∠BCO (Exterior angle) ∴ ∠ABO = 64 ........i) |
| Here |
In ΔAOB AO = BO (radius of the circle) So ∠OAB = ∠ABO = 64 ∴ ∠AOB = 180 - 128 = 52 |
| Hence |
∠AOD + ∠AOB + ∠BOC = 180 ⇒ ∠AOD + 52 + 32 = 180 ⇒ ∠AOD = 180 - 84 ⇒ ∠AOD = 96 |