In the figure, given below, AOB is a diameter of the circle and ∠AOC = 110°. Find ∠BDC.
Join AD. Here, `∠ADC = 1/2∠AOC = 1/2xx 110° = 55°` (Angle at the centre is double the angle at the circumference subtended by the same chord) Also, ∠ADB = 90° (Angle in a semicircle is a right angle) ∴ ∠BDC = 90° - ∠ADC = 90° - 55° = 35°
Solution In the Figure, Given Below, Aob is a Diameter of the Circle and ∠Aoc = 110°. Find ∠Bdc. Concept: Chord Properties - a Straight Line Drawn from the Center of a Circle to Bisect a Chord Which is Not a Diameter is at Right Angles to the Chord.