plzz help me with this maths question about circles?
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
How ACE and DBE are similar???
- Elizabeth MLv 78 years agoBest Answer
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.
- monvilleLv 43 years ago
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 ?