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:
∠BOX
Topic: Tangents / chords
Previous-year question practice database
Answer
Exam answer
OX ⟂ BX because radius OX is perpendicular to tangent BX. Thus ∠OXB = 90°.
Given ∠OBX = 32°. In ΔBOX: ∠BOX = 180° − 90° − 32° = 58°.
Answer: ∠BOX = 58°.
Explanation
∠BOX is the angle at O in right triangle BOX. OX is a radius and BX is tangent at X.
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