Question

In a triangle ABC right angled at B, AB =12cm, AC=13cm. Find BC.​

Answer 1

Answer:

B =90°

AB=12 cm

AC=13

By Pythagoras theorem

AC square = AB square + BC square

169 = 144 + BC square

BC square = 169 - 144

BC square = 25

BC = 5 cm

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Answer 2

In △ABC,

⇒ ∠B=90

o

[ Given ]

⇒ AB=12cm and AC=13cm [ Given ]

Here, O is center of a circle and x is a radius.

⇒ (AC)

2

=(AB)

2

+(BC)

2

[ By Pythagoras theorem ]

⇒ (13)

2

=(12)

2

+(BC)

2

⇒ 169=144+(BC)

2

⇒ (BC)

2

=25

∴ BC=5cm

Now, AB,BC and CA are tangents to the circle at P,N and M respectively.

∴ OP=ON=OM=x [ Radius of a circle ]

⇒ Area of △ABC=

2

1

×BC×AB

=

2

1

×5×12

=30cm

2

Area of △ABC= Area of △OAB+ Area of △OBC+ Area of △OCA

⇒ 30=

2

1

x×AB+

2

1

x×BC+

2

1

x×CA

⇒ 30=

2

1

x(AB+BC+CA)

⇒ x= AB+BC+cα/2×30

⇒ x= 12+5+13/60

⇒ x= 60/30

∴ x=2cm