Question

AB subtends angle Ô
1
= 38o
at O, the centre of the circle, and AO//BC. Determine the size
of OÂC.

Answer 1

We have given that AB subtends angle Ô 1 = 38o at O.

Since AO//BC, we can conclude that angle AOC is equal to angle Ô 1.

Therefore, angle AOC = 38o.

Now, we can use the fact that the angles in a triangle add up to 180o to find the size of OÂC.

In triangle OAC, we have

angle AOC + angle OAC + angle OCA = 180o.

Substituting the known values, we get

38o + angle OAC + angle OCA = 180o.

Simplifying the equation, we have

angle OAC + angle OCA = 180o - 38o = 142o.

Since angle OAC and angle OCA are equal in an isosceles triangle, we can divide the sum by 2 to find the size of each angle:

angle OAC = angle OCA = 142o/2 = 71o.

Therefore, the size of OÂC is 71o.