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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 radius of the circle is 5 cm. find the length of the equal chords.



A

102cm

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B

10 cm

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C

52cm

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D

5 cm

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Solution

The correct option is B

52cm


Given radius AO = 5 cm, then diameter AB =10 cm

In ΔACB

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

A=B (ABC is an isosceles traingle, AC = BC)

A+B+90=180

x+x+90=180x=45

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

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

12:12:1

1:1:2

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

The corresponding sides can be calculated as.

4545901:1:2x:x:x2ACCBAB525210

(x2 = 10,  x=102 = 52)

So, the chord AC =CB =52cm


Mathematics

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