A circle is inscribed in a quadrilateral ABCD in such a manner that the circle is tangent to all the four sides of the quadrilateral. It is given that Angle BAD = 90^{0}= Angle CBA.
Find the radius of the circle given that: BC = 21 units and AD = 28 units.
What would be the radius of the inscribed circle if BC = 36 units and AD = 45 units?
Let a = AD, b = BC, and r = radius of circle.
For a tangential quadrilateral we have
AB + CD = AD + BC
or
CD = AD + BC  AB = a + b  2r (1)
Applying the Pathagorean theorem we have
CD^2 = AB^2 + (AD  BC)^2
= (2r)^2 + (a  b)^2 (2)
Combining (1) and (2) gives
a*b
r = 
a + b
Case I: a = 28 and b = 21 gives r = 12.
Case II: a = 45 and b = 36 gives r = 20.

Posted by Bractals
on 20061231 12:23:31 