CAIE IGCSE Mathematics Extended E4.8 Circle Theorems Ii Topic Practice

NOT TO SCALE
P and Q are points on the circle with centre O.
TP and TQ are tangents to the circle from the point T.
Complete the following statements and reasons.
In triangles OPT and OQT
O P= ...... because each is a radius of the circle
OT is a common side

Angle O P T= angle ...... =90^ because ......
Triangles OPT and OQT are congruent using the criterion ......
This proves that the tangents TP and TQ are ......

NOT TO SCALE
P, Q and R are points on a circle.
ST is a tangent to the circle at R.

Another tangent from the point S touches the circle at V.

Give a geometrical reason why triangle SVR is isosceles.

NOT TO SCALE
ABDF is a parallelogram and BCDE is a straight line.
$A F=12 \mathrm{~cm}, A B=9 \mathrm{~cm}$, angle $C F D=40^{\circ}$ and angle $F D E=80^{\circ}$.

Explain why triangle CDF is isosceles.