terms-a","count":8,"nhsCategoryOrder":"$2e"} 30:{"order":"4.01B"} 2f:{"id":"dGVybToxODMyMw==","name":"Geometrical Terms {B}","slug":"geometrical-terms-b","count":2,"nhsCategoryOrder":"$30"} 20:["$21","$23","$25","$27","$29","$1b","$2b","$2d","$2f"] 1f:{"nodes":"$20"} 1d:{"id":"dGVybTo2Njk3","name":"Geometry","slug":"geometry","count":67,"nhsCategoryOrder":"$1e","children":"$1f"} 31:T7d9,

In the diagram, $$A$$, $$B$$ and $$C$$ lie on the circumference of a circle with centre $$O$$. Calculate the correct size of angle $$ACB$$.

$$∠ 𝑂𝐴𝐵 = 28^𝑜$$ (∵Being base angles of isosceles triangle AOB)
$$∠ 𝑂𝐴𝐵 + ∠ 𝐴𝑂𝐵 + ∠ 𝑂𝐵𝐴 = 180^𝑜$$ (∵Being the angles of a triangle)
$$28^𝑜 + ∠ 𝐴𝑂𝐵 + 28^𝑜 = 180^𝑜$$
$$∠ 𝐴𝑂𝐵 + 56^𝑜 = 180^𝑜$$
$$∠ 𝐴𝑂𝐵 = 124^𝑜$$

$$∠ 𝐴𝐶𝐵 = \frac12 × ∠ 𝐴𝑂𝐵$$ (∵The inscribed angle is half of the central angle on the same arc)
Hence $$∠ 𝐴𝐶𝐵 = \frac12 × 124^𝑜 = 62^𝑜$$
Calculate the values of angles $$x$$, $$y$$ and $$z$$.

4.07 - Circle Theorems I

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