23.03 Tangents to a circle
Interactive practice questions
In this question we aim to prove that the tangent is perpendicular to the radius drawn from its point of contact.
In the diagram, $C$C is an arbitrary point on the line $AD$AD, and $B$B is the point at which the tangent meets the circle.
What can we say about the lines $OB$OB and $OC$OC?
$OB=OC$OB=OC
$OB>OC$OB>OC
$OB
What point on $AD$AD is closest to the centre of the circle?
Point $A$A
Point $B$B
Point $C$C
Point $D$D
In general, what can we say about the angle of a line joining some point to some other line by the shortest route?
The angle is obtuse.
The angle is reflex.
The angle is a right angle.
The angle is acute.
Hence, what can we say about angle $\angle OBA$∠OBA?
Straight angle
Acute angle
Reflex angle
Right angle
Prove that $\triangle OAC$△OAC and $\triangle OBC$△OBC are congruent. Then, show that $AC=BC$AC=BC.
Prove that $y+z=x$y+z=x.
Consider the figure: