Question

QC and QD are the tangents to circle of center O from external point Q. If the distance between point Q and center of circle is 41 cm and radius of circle is 9 cm, find the length of tangent QD. 

1. 25 cm
2. 30 cm
3. 20 cm
4. 40 cm

Answer 1

Correct Answer - Option 4 : 40 cm

Given:

QC and QD are the tangents to circle of center O from external point Q.

QO = 41 cm

Radius of circle (OC) = 9 cm

Concepts used:

According to Pythagoras Theorem, in right angle triangle, the sum of square of perpendicular and base of triangle is equal to square of the hypotenuse.

Tangents from same external point to circle are equal to each other.

The angle between the tangent touching the circle and the radius of circle is 90°.

Calculation:

QC and QD are tangents from external point Q to circle with centre O.

⇒ QC = QD

In ΔQEO, applying Pythagoras theorem,

QO² = OC² + QC²

⇒ 41² = 9² + QC²

⇒ QC = 40 cm

⇒ QC = QD = 40 cm

∴ Length of tangent QD is equal to 40 cm.