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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 C 6 cm In Δ ABC ∠B=150∘, AC=3 cm Draw diameter AD and join CD to form quadrilateral ABCD ∠ ADC=180∘−150=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 30∘60∘90∘x:x√3:2x↓↓↓ACCDAD↓↓↓3 cm3√3 cm6 cm Hence diameter AD = 6 cm

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