Question

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Answer 1

△ABCisrightanglewhere∠A=90andAB=6cmandAC=8cm

Obethecenterofcircleandristheradiusofcircle

AB,BCandCAaretangentstocircleatP,NandM.

Areaof△ABC=

2

1

×AB×h

=

2

1

×6×8=24cm

2

Bypythagoreastheorm

BC

2

=AC

2

+AB

2

=8

2

+6

2

=64+36=100

BC=

100

=10

Area△ABC=Ar△OAB+Ar△OBC+Ar△OCA

24=

2

1

×r×AB+

2

1

×r×BC+

2

1

×r×CA

24=

2

1

r(AB+BC+CA)

48=r(6+8+10)

⇒r=

24

48

=2cm

Hope it helps!

Answer 2

Answer:

By Pythagoras theorem, BC= 10

Inradius = (a+b-c)/2 = (6+8-10)/2 = 2