A line from point A is drawn that is tangent to the circle at point B. A secant is also drawn from point A to the circle intersecting it at points C and D. If AB = 42 cm and AC = 21 cm, then what is the ratio between AB and CD?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 2 : 3.
Let CD = x, so
AD = AC + CD = 21 + x
Now,
⇒ AB2 = AC × AD
⇒ 422 = 21 × (21 + x)
⇒ 1764 = 21 × (21 + x)
⇒ 1764 = 441 + 21x
⇒ 21x = 1764 - 441
⇒ 21x = 1323
⇒ x = 63
So,
⇒ CD = x = 63
Now, The ratio AB/CD = 42/63 = 2/3 = 2 : 3