let ABCD be a quadilateral inscribd in a circle with diameter AC ,E be the foot of perpendicular from D onto AB as shown in the figure if AD=DC and the area of ABCD is 24 cm² .find the square length of DE(in cm)
Answers
ANSWER :
Let CD= x then AB = 2CD = 2x
Let r be the radius of the circle inscribed in the quadrilateral ABCD.
ar ( square ABCD ) = 18 and AB||CD
=> 1/2 (x+2x)2r = 18
=>3xr = 18
=> xr = 6. ------------------(1)
OP = OM = PD = OQ = AM = r
=> PC = x-r and MB = 2x-r
Let angle PCQ = angle OCQ = O
In right - angled ΔOPC,
tanΦ = OP/CP = r/x-r. -------------(2)
CD||AB
.°. angle PCB = angle QOM = 20
=> angle CBA = 180°- 20
=> angle OBM = 90° - 0
From ΔOMB
tan (90° - Φ) = OM/MB = r/2x-r
Right - angled ΔOBM,
tan Φ = 2x-r/r. --------------------(3)
From (2) and (3)
=> r/x-r 2x-r/r
=> 2x² - 3xr = 0
=> x(2x-3r) = 0
=> x=3r/2. ---------------------(4)
From (1) and (4)
=> xr = 6
=> 3xr/2 = 6
=> r² = 4
=> r= 2
- The value of r is 2
______Hope this will help you ______
Answer:
..............the top is the correct ANSWER