ΔABC is inscribed in a circle. A tangent is drawn to the circle at point A, intersecting the extension of side BC at D. If AD = 6 cm and CD = 4 cm, what is the length of side BC?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 5 cm.
DB = BC + CD = BC + 4
Tangent-secant theorem:
From point D, tangent AD and secant DB: AD2 = DB × DC
⇒ 62 = (BC + 4) × 4
⇒ 36 = 4(BC + 4)
⇒ 9 = BC + 4
⇒ BC = 5 cm