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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 ABO = 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

Identify the Relationship Between Angles

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Answer

Since BC is a tangent to the circle at point B, angle ABO (which is equal to x°) forms a right angle with line BC. Therefore, angle ABC is equal to 90°.

Step 2

Use the Angles in a Triangle

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Answer

In triangle ACB, the sum of the interior angles is 180°. We have:

$ext{Angle ACB} + ext{Angle ABC} + ext{Angle CAB} = 180°$

Substituting the known values:

$ext{Angle ACB} + 90° + (180° - x°) = 180°$

Step 3

Simplify the Equation

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Answer

Now, simplify the equation:

$ext{Angle ACB} + 90° + 180° - x° = 180°$

So, we can rearrange it to find angle ACB:

$ext{Angle ACB} = x° - 90° + 90° = 90° - x°$

Step 4

Final Answer

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Answer

Thus, the size of angle ACB in terms of x is:

$ext{Angle ACB} = 90° - x°$

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