AB is a diameter of a circle with centre O. CB is tangent to the circle at B. AC intersects the circle at G. If the radius of the circle is 6 cm and AG = 8 cm, then the length of BC is:
Show answer & explanation
Correct answer: C
Explanation
Correct Answer is option 3 i.e. 6√5 cm
Angle made by diameter at any point on the circle is 90°
Given
Radius = 6 cm and AG = 8 cm
Suppose ∠BAG = x°
As in the figure:
Triangle AGB is right angled
Hence, applying Pythagoras theorem:
BG = √(AB2-AG2)
⇒ BG = √(122- 82) = √80
⇒ BG = 4√5
Now, In triangle AGB and ABC:
Tan x = BG/AG = BC/AB
⇒ BC = BG/AG × AB
⇒ BC = 4√5/8 × 12
⇒ BC = 6√5 cm