Consider AD is a tangent to a circle of radius 6 cm. AC is a secant meeting the circle at B and CD is a diameter. If AB is 7 cm, then the value of AC (in cm) is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 16.
Radius = 6 cm
Diameter = 12 cm
We know that,
AD2 = AC × AB
By Pythagoras theorem
AC2 = AD2 + DC2
Now,
⇒ AC2 - DC2 = AC × AB
⇒ AC2 - 122 = AC × 7
⇒ AC2 - 144 = AC × 7
⇒ AC2 - 7AC - 144 = 0
⇒ AC2 - 16AC + 9AC - 144 = 0
⇒ AC(AC - 16) + 9(AC - 16) = 0
⇒ (AC - 16) (AC + 9) = 0
⇒ AC = 16, snd -9 [value can't be negative]
So, AC = 16 cm