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Ayush asked in Science & MathematicsMathematics · 8 years ago

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???

2 Answers

  • 8 years ago
    Best 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.

  • 3 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 ?

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