Question

AP is a tangent to the given circle. If AB = 8 cm and BC = 10 cm, then AP is:

Options

• 8 cm

• 16 cm

• 12 cm

• 24 cm

Answer 1

12 cm

Explanation:

We know that,

If a chord and a tangent intersect externally, then the product of the lengths of the segments of the chord is equal to the square of the length of the tangent from the point of contact to the point of intersection.

From figure,

AC = AB + BC = 8 + 10 = 18 cm.

⇒ AB × AC = AP²

⇒ 8 × 18 = AP²

⇒ AP² = 144

⇒ AP = `sqrt(144​)` = 12 cm.