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A, B, C and D are points on the circumference of a circle, centre O - OCR - GCSE Maths - Question 16 - 2017 - Paper 1

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A, B, C and D are points on the circumference of a circle, centre O. Angle BAD = 52°. (a) Work out angle x. Give a reason for your answer. x = ...................... show full transcript

Worked Solution & Example Answer:A, B, C and D are points on the circumference of a circle, centre O - OCR - GCSE Maths - Question 16 - 2017 - Paper 1

Step 1

Work out angle x.

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Answer

To find angle xx, we utilize the fact that the angle at the center of the circle is twice the angle at the circumference. This is a known property of circles.

Thus, we have:

x=2×52°=104°.x = 2 \times 52° = 104°.

Reason: The angle at the center is twice the angle at the circumference.

Step 2

Work out angle y.

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Answer

To find angle yy, we apply the property that opposite angles in a cyclic quadrilateral are supplementary. This means that the sum of angles yy and xx must equal 180°.

Therefore:

y=180°−x=180°−104°=76°.y = 180° - x = 180° - 104° = 76°.

Reason: Opposite angles in a cyclic quadrilateral are supplementary.

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