Two circles, centred at P and Q intersect at two points C and D. AB is tangent to the two circles at A and B. If = 68°, then = _____________.
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 112°.
∠ADB = 68°
Join C and D in the given figure.
∠BAC = ∠ADC [Angle in alternate segment]
Also, ∠ABC = ∠BDC [Angle in alternate segment]
∠BAC + ∠ABC = ∠ADC + ∠BDC
⇒ 180° - ∠ACB = ∠ADB
⇒ ∠ACB = 180° - ∠ADB
⇒ ∠ACB = 180° - 68° = 112°
Therefore, the value of ∠ACB is 112°.