Question

The circles are tangent to one another and each circle is tangent to the sides of the right triangle abc with right angle abc. If the larger circle has radius 12 and the smaller circle has radius 3, what is the area of the triangle​

Answer 1

Answer:

Correct option is

C

2

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

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