Question

ABC ia a right triangle right angles at B with side length |AB|=25, |BC|=50. If DBEF in the diagram is square, what is the area of DBEF

Answer 1

Answer:

AB = 5 cm, BC = 12 cm

Using Pythagoras theorem,

AC2=AB2+BC2

= 52+122

= 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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