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