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:
∠ZYX
Topic: Tangents / chords
Previous-year question practice database
Answer
Exam answer
Given ∠AXZ = 66°.
By the tangent–chord theorem: angle between tangent AX and chord XZ = angle in the alternate segment subtended by chord XZ.
Therefore: ∠ZYX = ∠AXZ = 66°.
Answer: ∠ZYX = 66°.
Explanation
∠AXZ is the tangent–chord angle at X; ∠ZYX is the angle in the alternate segment standing on chord XZ.
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