Q. 73.8( 5 Votes )

In the picture, A

Answer :

Let O be the center of a circle


Join BC, OA, OB, OC and OD


Given: AB CD


In Δ ABK


ABC + BCD + BKC = 180° (Angle sum property)


ABC + BCD + 90° = 180°


ABC + BCD = 90° …..(1)


AOC = 2 ABC ( angle at center twice angle in


segment) ...(2)


BOD = 2 BCD ( angle at center twice angle in


segment) ...(3)


Adding (2) and (3)


AOC + BOD = 2 ABC + 2 BCD


AOC + BOD = 2 ( ABC + BCD)


AOC + BOD = 2 × 90° (from (1))


AOC + BOD = 180°



Hence, (angle at center is half of 360° )


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