Question

Diagram NOT

accurately drown
28
A, B and Care points on a circle, centre 0
Angle ABC = 389
Work out the size of angle OAC
Give a reason for each stage of your working

Answer 1

m(∠OAC) = 52°

Explanation:

A, B and C are the pints on a circle with center O.

m(∠ABC) = 38°

By the central angle theorem,

"Central angle subtended by two points on a circle measure the twice of the inscribed angle subtended by these points."

m(∠AOC) = 2m(∠ABC)

m(∠AOC) = 2 × 38° = 76°

Now in ΔAOC,

AO and OC are the radii, so the angles opposite to radii will measure the same.

∠OAC ≅ ∠OCA

Since, sum of all the interior angles of a triangle is 180°.

m(∠OAC) + m(∠OCA) + m(∠AOC) = 180°

m(∠OAC) + m(∠OAC) + 76° = 180°

2m(∠OAC) = 180° - 76°

2m(∠OAC) = 104°

m(∠OAC) = 52°