In the given figure, two circle intersect at `A` and `B`. The centre of the smaller circle is `O` and lies on the circumference of the larger circle.
If `PAC` and `PBD` are straight lines and `/_ APB = 70^(@)`, find
(i) `/_ AOB, (ii) /_ ACB` and (ii) `/_ADB`.

Explanation

(i) Minor arc `AB` subtends `/_ AOB` at the centre and `/_ APB`, a point on the remaining part of the circle.
`:. /_ AOB = 2 /_APB = 2 xx 70^(@) = 140^(@)`
(ii) `AOBC` is a cyclic quadrilateral.
`:. /_ AOB + /_ ACB = 180^(@)`
`implies 140^(@) +/_ ACB = 180^(@)`
`implies /_ ACB = 180^(@) -140^(@) = 40^(@)`
(iii) `/_ ADB = /_ ACB = 40^(@)` `[ /_ s` is the same segment ].