Question

If ABC is a right angled triangle and angle B is a right angle ,if AB=5 BC=12 then find the value of C​

Answer 1

Step-by-step explanation:

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Asked on October 15, 2019 by

Rïdhïma Basha

In a right triangle ABC, right-angled at B,BC=12cm and AB=5cm. The radius of the circle inscribed in the triangle (in cm) is

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VIDEO EXPLANATION

ANSWER

Given:

AB = 5 cm, BC = 12 cm

Using Pythagoras theorem,

AC

2

=AB

2

+BC

2

= 5

2

+12

2

= 25+144

= 169

AC=13.

We know that two tangents drawn to a circle from the same point that is exterior to the circle are of equal lengths.

So, AM=AQ=a

Similarly MB=BP=b and PC=CQ=c

We know

AB=a+b=5

BC=b+c=12 and

AC=a+c=13

Solving simultaneously we get a=3,b=2 and c=10

We also know that the tangent is perpendicular to the radius

Thus OMBP is a square with side b.

Hence the length of the radius of the circle inscribed in the right angled triangle is 2cm.

solution