Question

The sides containing the right angle of a right angled triangle are 12 cm and
16 cm respectively. What is the radius of the circumcircle of this triangle?
(1) 12 cm (2) 10 cm (3) 8 cm (4) 6 cm
for which​

Answer 1

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.