In the figure, given below, P and Q are the centres of two circles intersecting at B and C ACD is a straight line. Calculate the numerical value of x .
∠ACB = ` 1/2 ∠APB =1/2 xx 150 = 75° ` (Angle at the centre is double the angle at the circumference subtended by the same chord) ∠ACB + ∠BCD =180° (Straight line) ⇒ ∠BCD =180° - 75° =105° Also, ∠BCD =`1/2 `= reflex ∠BQD =`1/2` (360° - x )
(Angle at the center is double the angle at the circumference subtended by the same chord) x ⇒ 105 = 180° ∴ x = 2 (180 ° -° ) = 2 ×75 = 150°
Solution In the Figure, Given Below, P and Q Are the Centres of Two Circles Intersecting at B and C Acd is a Straight Line. Calculate the Numerical Value of X. Concept: Arc and Chord Properties - the Angle that an Arc of a Circle Subtends at the Center is Double that Which It Subtends at Any Point on the Remaining Part of the Circle.