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India
Class IX

Tangents to Circles

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 centre 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

Prove that $\triangle OAC$OAC and $\triangle OBC$OBC are congruent. Then, show that $AC=BC$AC=BC.

Easy
6min

Prove that $y+z=x$y+z=x.

Easy
6min

Consider the figure:

Easy
1min
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Outcomes

9.G.T.1

Two triangles are congruent if any two sides and the included angle of one triangle is equal to any two sides and the included angle of the other triangle (SAS Congruence). Two triangles are congruent if any two angles and the included side of one triangle is equal to any two angles and the included side of the other triangle (ASA Congruence). Two triangles are congruent if the three sides of one triangle are equal to three sides of the other triangle (SSS Congruence).

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