Draw two circles of radii 6 cm and 4 cm. From a point on the outer circle, draw a tangent to the inner circle and measure its length.

Open in App

Solution

Let AC be the tangent from outer circle on inner circle.
Then, in triangle OAC by pythagoras theorem,
$O A^{2} = O C^{2} + A C^{2}$
$A C^{2} = O A^{2} - O C^{2}$
$A C^{2} = 6^{2} - 4^{2}$
$A C^{2} = 20$
$A C = 2 \sqrt{5}$ cm

Suggest Corrections

Similar questions

Draw 2 concentric circles of radii 3cm and 5cm. Draw tangents to the inner circle from any point on the outer circle. Measure the length of the tangent. [4 MARKS]

Q. Draw two concentric circles of radii 4 cm and 6 cm. Construct a tangent to the smaller circle from a point on the larger circle. Measure the length of this tangent.

Q. Draw two concentric circles of radii 2 cm and 6 cm. Taking a point on the outer circle, construct a pair of tangents to the other. Measure the lengths of the two tangents. [4 MARKS]

Draw two concentric circles of radii 3 cm and 5 cm. Taking a point on the outer circle, construct the pair of tangents to the inner circle.

Q. Draw two concentric circles of radii 3 cm and 5 cm. Taking a point on outer circle construct the pair of tangents to the other. Measure the length of a tangent and verify it by actual calculation.

Join BYJU'S Learning Program

Draw two circles of radii 6 cm and 4 cm. From a point on the outer circle, draw a tangent to the inner circle and measure its length.

Let AC be the tangent from outer circle on inner circle.Then, in triangle OAC by pythagoras theorem,OA2=OC2+AC2AC2=OA2−OC2AC2=62−42AC2=20AC=2√5 cm

Let AC be the tangent from outer circle on inner circle.
Then, in triangle OAC by pythagoras theorem,
$O A^{2} = O C^{2} + A C^{2}$
$A C^{2} = O A^{2} - O C^{2}$
$A C^{2} = 6^{2} - 4^{2}$
$A C^{2} = 20$
$A C = 2 \sqrt{5}$ cm