1 of 3

CIRCLE

  • Sum based on Theorem – The lengths

of two tangents drawn from

an external point to a circle are equal.

2 of 3

N

L

M

C

A

B

O

Q. ABC is a right triangle right-angled at A such that AB = 6 cm

and AC = 8 cm. Find the radius of its incircle.

Sol.

r

r

r

6cm

8cm

In ΔABC,

m ∠CAB

= 90°

∴ CB2

CA2

+

AB2

=

[By Pythagoras theorem]

∴

CB2

82

+

62

=

∴

CB2

64

+

36

=

∴

CB2

100

=

∴

CB

10cm

=

[Taking square roots]

Let the radius of the circle be r

OL = OM = ON = r

[Radii of the same circle]

Seg OL ⊥ side AB

Seg OM ⊥ side BC

[Radius is perpendicular to the tangent]

Seg ON ⊥ side AC

...(i)

...(ii)

10 cm

Draw OL, ON and OM

∠A = 90º

We know that, Radius is perpendicular to tangent

Consider ΔABC

3 of 3

Q. ABC is a right triangle right-angled at B such that AB = 6 cm and AC = 8 cm. Find the radius of its incircle.

Sol.

ar (ΔABC)

[Area Addition Property]

×

1

2

= 3r cm2

= 4r cm2

= 5r cm2

ar (ΔAOB)

=

ar (ΔAOC)

ar (ΔBOC)

ar (ΔAOB)

+

ar (ΔBOC)

+

ar (ΔAOC)

=

3r

+ 5r

+ 4r

=

24

∴

12r

∴

=

24

r = 2

∴

× AB

1

2

ar (ΔAOB)

=

Similarly,

1

2

= 24 cm2

ar (ΔABC)

=

∴

N

L

M

C

A

B

O

6cm

10 cm

6

r

×

×

8

6

×

8cm

r

r

× OL

r

Also,

What is the formula to find area of triangle ?

× base × height

1

2

Area of triangle

=

Consider ΔAOB

ΔABC is made up of 3 triangles

ΔAOB, ΔBOC, ΔAOC