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:
∠CYX
Topic: Circle theorems
Previous-year question practice database
Answer
Exam answer
∠COX = ∠BOX = 58°.
∠COX is the angle at the centre subtended by arc CX. ∠CYX is the angle at the circumference subtended by the same arc CX.
∠COX = 2∠CYX 58° = 2∠CYX ∠CYX = 29°.
Answer: ∠CYX = 29°.
Explanation
The angle at the centre is twice the angle at the circumference standing on the same arc CX.