P, Q and R are points on the circumference of a circle, centre O - OCR - GCSE Maths - Question 17 - 2023 - Paper 4
Question 17
P, Q and R are points on the circumference of a circle, centre O.
Angle PRQ = 59° and angle PQR = 67°.
Line SPT is a tangent to the circle.
(i) Work out angle a.
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Worked Solution & Example Answer:P, Q and R are points on the circumference of a circle, centre O - OCR - GCSE Maths - Question 17 - 2023 - Paper 4
Step 1
Work out angle a.
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Answer
Angle a = 67° because it is equal to angle PQR (the angle in the same segment).
This follows from the property that angles in the same segment of a circle are equal.
Step 2
Work out angle b.
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Answer
Angle b = 59° because it is equal to angle PRQ (the angle subtended by the same arc).
This follows from the fact that angles subtended by the same chord at the circumference are equal.
Step 3
Complete the following, giving the values of the angles in terms of x.
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Answer
Obtuse angle EOG = 180° - x because it is supplementary to acute angle EHG.
Write down what your working in part (b)(i) has proved.
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Answer
The calculations show that the angles in the cyclic quadrilateral relationship provide consistency in their measures, indicating that opposite angles sum to 180°.
