Question bankCircle Theorems

Circle Theorems

A circle with centre O contains triangle UVW with UV and VW marked equal, tangent XWY at W, radii OV and OW, and angle XWU labelled θ°.

$U$ , $V\,$ and $W\,$ are points on a circle, centre $O$ . $XWY\,$ is a tangent to the circle at $W$ .

$U V = V W$ Angle $\theta^\circ$

Find the size of angle $O W V$ , in terms of $θ\theta$ . Give reasons for each stage of your working.

[5]

Question bankCircle Theorems

A circle with centre O contains triangle UVW with UV and VW marked equal, tangent XWY at W, radii OV and OW, and angle XWU labelled θ°.

$U$ , $V\,$ and $W\,$ are points on a circle, centre $O$ . $XWY\,$ is a tangent to the circle at $W$ .

$U V = V W$ Angle $\theta^\circ$

Find the size of angle $O W V$ , in terms of $θ\theta$ . Give reasons for each stage of your working.

[5]

Circle Theorems Questions