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Question

AC and BC are two equal chords of a circle with diameter AB forming a ΔABC as shown in the figure. If the equal chords have length 20 cm, then the area of the circle is equal to


A

50 π cm2

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B

100 π cm2

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C

200 π cm2

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D

150 π cm2

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Solution

The correct option is C

200 π cm2


In the given above figure, triangle ABC is isosceles (AC = BC) given

ACB=90 (angle subtended by diameter AB on circumference)

A+B+90=180 (sum of angles of a triangle)

2x+90=180(A=B. say x as triangle is isosceles)

x=45

Now, angle of tirangle ABC are 45,45,90

sin(45):sin(45):sin(90)

12:12:1

1:1:2

So, sides AC, CB, AB will be in ratio 1:1:2

So, the corresponding sides will be calculated as

4545901:1:2ACCBAB20cm20cm202cm

Diameter AB=202cm, radius =102cm

Area =πr2=π(102)2=200π cm2


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