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12.06 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.

a

What can we say about the lines $OB$OB and $OC$OC?

$OB=OC$OB=OC

A

$OB>OC$OB>OC

B

$OBOB<OC

C
b

What point on $AD$AD is closest to the center of the circle?

Point $A$A

A

Point $B$B

B

Point $C$C

C

Point $D$D

D
c

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.

A

The angle is reflex.

B

The angle is a right angle.

C

The angle is acute.

D
d

Hence, what can we say about angle $\angle OBA$OBA?

Straight angle

A

Acute angle

B

Reflex angle

C

Right angle

D
Easy
1min

In the figure below, $AC$AC is tangent to both circles.

Easy
2min

In the diagram, $AC$AC is a tangent to the circle with center $O$O. What is the measure of $x$x?

Easy
< 1min

If $\overline{BA}$BA is a tangent to the circle, determine the value of $x$x showing all steps of working.

Easy
1min
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Outcomes

II.G.C.2

Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.

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