23.03 Tangents to a circle
In the diagram, C is an arbitrary point on the line AD, and B is the point at which the tangent meets the circle.
What can be said about the lengths of OB and OC?
What point on AD is closest to the centre of the circle?
In general, what can be said about the angle of a line joining some point to some other line by the shortest route?
Hence, what can be said about angle \angle OBA?
Consider the following figure:
Show that \angle OBP is a straight angle.
Hence what can we say about points O, B and P?
Find the value of the pronumerals in the following diagrams. Give reasons for your answer.
The circle in the following diagram has a radius of 8 and AB has a length of 9 units.
Calculate the length of FE.
In the diagram, TU and TV are tangents to the circle with centre O. Find the size of \angle SUV.
In the following diagram, JL is a tangent to the circle with centre O. JO = 29 and JK = 20. Find the length of the radius OK.
In the following diagram, PA and PB are two tangents issued from point P to the circle of center O, such that \angle PBO=37.
Find the value of y.
Find the value of x.
Find the value of the pronumerals in the following diagrams. Give reasons for your answer.
In the following diagram, PA and PB are two tangents issued from point P to the circle of center O, such that PB=5.
Find the value of x.
Find the value of y.
In the diagram, PT is a tangent to the circle. Find the size of \angle YZT.
In the figure, O is the center of the circle, PA and PB are tangents. Find the size of \angle APB if \angle OAQ=56\degree.
In the diagram, PT is a tangent to the circle with centre O. Determine the value of b.
In the following diagram, AB, BC and AC are tangents to the circle. BD = 7 \text{ cm}, AF = 6 \text{ cm}, and BC = 11 \text{ cm}. Find p, the perimeter of \triangle ABC.
In the diagram, PT is a tangent to the circle. Determine the value of f.
Prove that \triangle OAC and \triangle OBC are congruent. Then, show that AC = BC.
For the following diagram, prove that \\ y + z = x.
For the following diagram, prove that \\ AB \parallel FG.
