Question

In the above figure (not to scale), O is the centre of the circle. `bar(AP)` and `bar(BP)` are two chords. C is the point of intersection of `bar(AP)` and `bar(OB)`. If `/_ OAC= 30^(@)` and `/_ PBC =80^(@)`, then `/_ AOB=`
A. `110^(@)`
B. `100^(@)`
C. `130^(@)`
D. `120^(@)`

Answer 1

Correct Answer - B
(i) Sum of the angles of a triangle is `180^(@)`. Vertically opposite angles are equal.
(ii) Use the relation `/_APB =(1)/(2) /_ AOB =x`.
(iii) `/_OCA = /_ PCB . ` ( as they are vertically opposite angles )
(iv) Sum of the angles of a triagnel is `180^(@)`.