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
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