Try this beautiful problem from Geometry based on the radius and tangent of a circle.
As shown in the figure below ,circles $C_1 $and$ C_2$ of radius 360 are tangent to each other , and both tangent to the straight line l.if the circle$ C_3$ is tangent to $C_1$ ,$C_2$ and l ,and circle$ C_4 $is tangent to$ C_1$,$C_3$ and l ,find the radius of$ C_4$
Geometry
Pythagoras theorm
Distance Formula
Answer:40
SMO -Math Olympiad-2013
Pre College Mathematics
Let R be the radius of $C_3$
$C_2E$ =360-R
$C_3E=360$
$C_2C_3$=360+R
Using pythagoras theorm ....
$ (360-R)^2+360^2=(360+R)^2$
i.e R=90
Can you now finish the problem ..........
Let the radius of$ C_4$ be r
then use the distacce formula and tangent property........
can you finish the problem........
Let r be the radius of $C_4$ (small triangle).
LO+OC=360
$\sqrt{(360+p)^2-(360-p)^2}+\sqrt{(90+r)^2-(90-r)^2}=360$
i.e r=40.
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