Question

Construct tangents to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and find its approximate length.

• A. 3 cm
• B. 4.5 cm
• C. 3.5 cm
• D. 4 cm

Answer 1

The correct option is B

4.5 cm

Draw two concentric circles with radii 4 cm and 6 cm and mark its centre as O.

Mark a point P on the outer circle. Join OP.

Construct the perpendicular bisector of OP which intersects OP at point O’.

Taking O’P as radius, draw another circle. Let it intersect the inner circle at Q and R.

From point P, draw tangents PQ and PR; as shown in figure.

Measure PQ and PR. PQ = PR = 4.5 cm (approx)

Verify using Pythagoras theorem:

$P{Q}^2=O{P}^2-O{Q}^2$

$=6^2-4^2$

$=36-16=20$

Or, PQ = 4.5 cm (approx)