A, B, C and D are points on the circumference of a circle, centre O - OCR - GCSE Maths - Question 16 - 2017 - Paper 1
Question 16
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.
96%
114 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
To find angle x, 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°.
Reason: The angle at the center is twice the angle at the circumference.
Step 2
Work out angle y.
99%
104 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
To find angle y, we apply the property that opposite angles in a cyclic quadrilateral are supplementary. This means that the sum of angles y and x must equal 180°.
Therefore:
y=180°−x=180°−104°=76°.
Reason: Opposite angles in a cyclic quadrilateral are supplementary.
