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 angle... 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 that the ratio of the sizes of angles BCD and BAD is 3:1, let the size of angle BCD be represented as 3x and the size of angle BAD as x. Hence, we have:
3x+x=180°
Solving for x gives:
\Rightarrow x = 45°$$
Thus, angle BCD is:
$$3x = 3(45°) = 135°.$$
Step 2
Find angle SBA
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Answer
Since SBT is a tangent to the circle and BD is a chord, angle SBA is formed by the tangent and the chord. By the Alternate Segment Theorem:
