Mathematics 0580: CIRCLE THEOREM Topical Past Paper Questions

NOT TO SCALE $P$, $Q$ and $S$ are points on a circle, centre $O$. $RT$ is a tangent to the circle at $S$. Find the ratio $\text{angle } PSO : \text{angle } PQO$. Give your answer in its simplest form. angle $PSO$ : angle $PQO$ = ........................ : ........................…

A, B and C lie on a circle centre O. DE is a tangent to the circle at C. Angle $ABC = 52^{\circ}$ and angle $BCE = 65^{\circ}$. (a) Find the value of x. Give a geometrical reason for your answer. x = because [2] (b) Find the value of y. y = [2]

A, B, C and D are points on a circle. ADX and BCX are straight lines. Angle $BAD = x^{\circ}$ and angle $DCX = y^{\circ}$. (a) Explain why $x = y$. Give a geometrical reason for each statement you make. [2] (b) Show that triangle $ABX$ is similar to triangle $CDX$. [2] (c) $AD =…