Q. 14.5( 15 Votes )

(i) In Figure (1), is the center of the circle. If and find (ii) In figure (2), and are three points on the circle with center such that and Find


Answer :



(i) Join OB.


OAB = OBA = 40°[Because OB = OA]


OCB = OBC = 30°[Because OB = OC]


ABC = OBA + OBC


ABC = 40°+ 30°


ABC = 70°


AOC = 2 × ABC


AOC = 2 × ABC


AOC = 2 × 70°


AOC = 14


(ii)


BOC = 360° - (AOB + AOC) [Sum of all angles at a point = 360°]


BOC = 360° - (90° + 110°)


BOC = 360° - 200°


BOC = 160°


We know that BOC = 2 × BAC


BAC = (1/2) × BOC


BAC = (1/2) × 160°


BAC = 8


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