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 = 900= 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|
|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
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 2006-12-31 12:23:31