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Question

One angle of a ΔABC is 150 and its opposite side is 3 cm as shown in the figure. The diameter of its circumcircle is equal to


A

63 cm

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B

62 cm

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C

6 cm

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D

33 cm

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Solution

The correct option is A

6 cm


In Δ ABC

B=150, AC=3 cm

Draw diameter AD and join CD to form quadrilateral ABCD

ADC=180150=30 (ABCD is the cyclic quadrilateral)

ACD=90 (Angle subtended by the diameter on the circumference)

Angles of triangle ADC are 30, 60, 90

The corresponding sides can be calculated as

sin(30):sin(60):sin(90)

12:32:1

1:3:2

306090x:x3:2xACCDAD3 cm33 cm6 cm

Hence diameter AD = 6 cm


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