4MA0 Higher June 2015 Paper 4R Q17

EdexcelHigherOld spec5 marksCircle Theorems

17 \(J\), \(K\), \(L\) and \(M\) are points on the circumference of a circle.
\(GJH\) is the tangent to the circle at \(J\).
\(MK\) and \(JL\) intersect at the point \(P\).
\(GML\) is a straight line.
Angle \(HJK = 62^\circ\), angle \(JKM = 21^\circ\) and angle \(JGL = 78^\circ\)

Circle through J, K, L and M with tangent GJH at J; chords MK and JL meet at P; GML a straight line; angles 62, 21 and 78 degrees marked

Diagram NOT accurately drawn

(a) Write down the size of angle \(MLJ\). (1)
(b) Write down the size of angle \(JLK\). (1)
(c) Work out the size of angle \(KPL\). (3)