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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) ⇒1√2:1√2:1 ⇒1:1:√2 So, sides AC, CB, AB will be in ratio 1:1:√2 So, the corresponding sides will be calculated as 45∘45∘90∘1:1:√2ACCBAB↓↓↓20cm20cm20√2cm Diameter AB=20√2cm, radius =10√2cm Area =πr2=π(10√2)2=200π cm2

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