Question

Draw a circle of radius 6 cm. Construct the two tangents to the circle from a P which is at the distance of 9 cm from centre. Measure the length of the tangents.

• A. 4.7 cm
• B. 6.7 cm
• C. 7.7 cm
• D. 5.7 cm

Answer 1

The correct option is B

6.7 cm

Draw a circle of radius 6 cm and mark its centre as O.

Mark a point P outside the circle such that OP is 9 cm.

Join OP.

Bisect OP at C.

Taking C as centre and OC as the radius draw a circle which intersect the previous circle at T and T’.

Join PT and PT’ which are the required tangents. Measure PT and PT’. It will be equal to 6.7 cm (approx.)

Alternate Method -
Since OT is perpendicular to TP
We can use Pythagoras Theorem, In $△OTP$
$P{T}^2=9^2-6^2$

PT = $\sqrt{45}$ = 6.7 cm