Question

In the given figure, AB and AC are tangents to a circle with centre O and radius 8 cm. If OA=17 cm, then the length of AC (in cm) is

Answer 1

AB and AC are the two tangents of the circle.

OB and OC are the radii of the circle and we know that radius of the circle is perpendicular to the tangent at the point of contact.

∴ OB ⊥ AB and OC ⊥ AC.

BY PYTHAGORAS THEOREM IN Δ AOC ,

OA² = OC² + AC²

⇒ ( 17 )² = ( 8 )² + AC²

⇒289 - 64 = AC²

⇒AC² =225

⇒ AC = 15

∴ LENGTH OF AC = 15 cm