In a circle with center O, the diameter AB extended to the point C, outside the circle. CD is a tangent at the point D on the circle. If the radius of circle is 6 cm and ∠DBC = 120°, then the length of CD is equal to:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. cm.
Given that, radius of circle = 6 cm
∠DBC = 120°
According to the given question,
OB = OD = 6 cm
Also, ∠DBC = 120°
⇒ ∠DBO = 60°
⇒ Triangle DOB is an equilateral triangle.
⇒ DB = 6 cm
Now, in triangle DBC, ∠BDC = ∠CDB = 30°
⇒ Triangle DBC is an isosceles triangle.
⇒ DB = BC = 6 cm
Now, BC × AC = CD2
⇒ 6 × 18 = CD2
⇒ CD2 = 108
⇒ CD =