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Points B, D, E and F lie on a circle - Edexcel - GCSE Maths - Question 15 - 2020 - Paper 3

Question 15

Points B, D, E and F lie on a circle. ABC is the tangent to the circle at B. Find the size of angle ABD. You must give a reason for each stage of your working.

Worked Solution & Example Answer:Points B, D, E and F lie on a circle - Edexcel - GCSE Maths - Question 15 - 2020 - Paper 3

Step 1

Find the size of angle DFB

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Answer

Since ABC is the tangent at point B, angle DFB is equal to angle EDB (which is 100°) because angles in the same segment are equal.

Step 2

Calculate angle DBE

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Answer

Now we can find angle DBE using the fact that angles in a cyclic quadrilateral add up to 180°:

$ext{Angle DBE} = 180° - (100° + 40°) = 40°$

Step 3

Determine angle ABD

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Answer

Angle ABD is equal to angle DBE, therefore:

$ext{Angle ABD} = 40°$

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