Higher June 2017 Paper 6 Q13 – Westie's Workshop

Higher June 2017 Paper 6 Q13

OCRHigherCurrent spec4 marksCircle Theorems Similar Shapes

13 A and B are points on the circumference of a circle, centre O.
CA and CB are tangents to the circle.

Circle centre O with points A and B on the circumference; tangents CA and CB meet at C outside the circle; lines OA, OB and OC are drawn

Not to scale

Prove that triangle OAC is congruent to triangle OBC. [4]

Mark scheme

Answer	Marks	Part marks and guidance
Three of these OC is common or shared OA = OB (equal) radii \(\angle\)OAC = \(\angle\)OBC tangent perpendicular to radius CA = CB tangents from a point [to a circle]	M3	M1 for each After M0, B2 three pairs of these equal sides/angles with insufficient or no reasons or B1 for two pairs of these equal sides/angles identified with insufficient or no reasons OR After M1, B1 for two further pairs of these equal sides/angles identified with insufficient or no reasons	Ignore extra facts and reasons For B marks accept if indicated on diagram
RHS, SSS or SAS as appropriate	A1

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