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A and B are points on a circle, centre O - Edexcel - GCSE Maths - Question 11 - 2018 - Paper 1

Question 11

A and B are points on a circle, centre O. BC is a tangent to the circle. AOC is a straight line. Angle ABD = x°. Find the size of angle ACB, in terms of x. Give yo... show full transcript

Worked Solution & Example Answer:A and B are points on a circle, centre O - Edexcel - GCSE Maths - Question 11 - 2018 - Paper 1

Step 1

Find the angle AOB

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Answer

Given that AB is a chord and OC is the radius to the tangent BC, angle ABC is an angle at the circumference subtended by chord AB. By the tangent-secant theorem, angle AOB is twice the angle ABD:

$AOB = 2x$

Step 2

Find the angle ACB

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Answer

Angle ACB is an exterior angle for triangle AOB. Therefore, it can be calculated as:

$ACB = \frac{1}{2}AOB = \frac{1}{2}(2x)$

Thus,

$ACB = x$

Step 3

Final answer

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Answer

The size of angle ACB, in terms of x, is:

$ACB = x$

This is in its simplest form.

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