Question

16. In a ∆ ABC ,right angled at B ,AC=22 cm and AB= 11cm ,find ∠A and ∠C ​

Answer 1

Your 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.

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