Higher June 2022 Paper 4 Q12

OCRHigherCurrent spec7 marksCircle Theorems

12

(a) Points A, B and C lie on the circumference of a circle.
EAF is a tangent to the circle.
Triangle ABC inscribed in a circle with tangent EAF at A; at A the angle between AF and AB is 53°, angle BAC is 78° and the angle between AC and AE is 49°

Not to scale

Write down the value of angle BCA giving a reason for your answer. [2]

(b) Points G, H and J lie on the circumference of a circle, centre O.
Circle centre O with points G, H and J on the circumference; lines OJ, OG, JG, JH and GH drawn; angle GOJ is 52° and angle GJH is x°; arrows show JO parallel to GH

Not to scale

Angle GOJ = 52° and angle GJH = \(x\)°.
Lines JO and GH are parallel.

Find the value of \(x\).
You must show your working. [5]

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