# plzz help me with this maths question about circles?

http://picturepush.com/host.php?image=7941710

This is the diagram

PlzzzTake some tyrouble and do answer my question

in the question

AE = 12 units

DE = 4 units

EC = 6 units

And AE is perpendicular to DC

Find the area of the circle

Plzzz help me

Update:

How ACE and DBE are similar???

Relevance

Triangles ACE and DBE are similar so AE/DE=BC/EB giving EB=2

From triangle AEC, where angle E is presumably 90 deg, tanA=6/12=1/2

From Pythagoras to triangle CEB, CB=sqrt(6^2+2^2)=sqrt(40).

If R is the radius of the circle, which is the circumcircle of triangle ABC,

a/sinA=2R, a=BC=sqrt(40), tanA=1/2 so sinA=1/sqrt(5) and 2R=sqrt(40)/(1/sqrt(5)

=sqrt(200)=10sqrt(2) so R=5sqrt(2). Area =piR^2=50pi.

You need familiarity with quite a bit of geometry and trigonometry for this question.

• Your query is alternatively doubtful .. Please re-sort are you handling one circle ? or Two ? and is the intercepted arc from a directly line intersecting the circle (s) , or from a different circle ?