NumericalEasy1 mark
9(iii)
X, Y, Z and C are the points on the circumference of a circle with centre O. AB is a tangent to the circle at X and ZY = XY. Given ∠OBX = 32° and ∠AXZ = 66°. Find:
∠OXY
Topic: Tangents / chords
Previous-year question practice database
Answer
Exam answer
ZY = XY, so ΔZXY is isosceles.
∠ZYX = 66°. Let ∠ZXY = ∠XZY = a.
2a + 66° = 180° a = 57°.
By the tangent–chord theorem: ∠YXB = ∠XZY = 57°.
OX ⟂ XB, so ∠OXB = 90°.
∠OXY = 90° − 57° = 33°.
Answer: ∠OXY = 33°.
Explanation
ZY=XY gives equal base angles at X and Z. The tangent–chord theorem then connects ∠XZY with the angle between chord XY and tangent XB.
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