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A, B, C and D are four points on a circle - Edexcel - GCSE Maths - Question 15 - 2021 - Paper 2

Question 15

A, B, C and D are four points on a circle. SBT is a tangent to the circle. Angle ABD = 20° the size of angle BAD: the size of angle BCD = 3:1 Find the size of angl... show full transcript

Worked Solution & Example Answer:A, B, C and D are four points on a circle - Edexcel - GCSE Maths - Question 15 - 2021 - Paper 2

Step 1

Find angle BCD

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Answer

Given the ratio of the angles, let the size of angle BCD be represented as ( x ). Therefore, angle BAD will be ( 3x ) according to the given ratio ( 3:1 ).

Since angles BCD and BAD are on the same arc, we can set up the equation:

$x + 3x = 180°$

This simplifies to:

$4x = 180°$

Solving for x gives us:

$x = 45°$

So, angle BCD = 45°.

Step 2

Find angle BAD

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Answer

Using the earlier calculation, angle BAD is:

$BAD = 3x = 3 \times 45° = 135°.$

Step 3

Find angle SBA

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Answer

Now, angle SBA can be calculated using the following relationship involving a tangent and a chord:

The angle formed between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.
Therefore, angle SBA = angle BCD.

Thus, we have:

$SBA = 45°.$

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