From point A, a tangent line is drawn to the circle of radius 7 units. From the same point, a secant is drawn to the circle, which cuts the circle at B and C, and the point B is near A than C. What is the length of BC (in units) if the length of the tangent to the circle from point A is 21 units and the length of AB is 14 units?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 17.5.
Let BC = x units, then AC = x + 14 units
According to the tangent-secant theorem,
AT2 = AB × AC
⇒ 212 = 14(14 + x)
⇒ 441 = 196 + 14x
⇒ 14x = 441 - 196 = 245
⇒ x = 245/14 = 17.5
Therefore, the length of BC is 17.5 units.