In the figure 35, angle ADC = 90 degrees, BC=38cm, CD=28cm and BP=25cm. Find the radius of the circle.

Given : angle ADC = 90 degrees
BC = 38cm , CD = 28cm , BP = 25cm
To Prove : to find radius
Construction : Join OR and OS
Proof : angle D = 90degree
Now OS is perpendicular to DA
= Angle OSD = 90 degree
Now OR is perpendicular to CD
= Angle ORD = 90 degree
=> ORDS is square as each angle is 90 degrees
Now ; From B : BP = BQ = 25cm
CQ = BC - BQ
= 38 - 25 = 13 cm
From C : CQ = CR = 13 cm
RD = DC - CR
RD = 28 - 13 = 15 cm
As ORDS is square and square has all sides equal .
So RD = RO = OS = DS = 15cm
Radius = OS = 15cm