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, as they are corresponding angles when line SPT is a tangent to the circle.
Step 2
Work out angle b.
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Answer
Angle b = 59° because it is equal to angle PRQ, as angles in the same segment of a circle 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 the external angle at point O, opposite to angle EHG.
