Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length. Also verify the measurement by actual calculation.

Question

Philoid · Accepted Answer

Steps of construction:

i. Draw two concentric circles with radii 4 cm and 6 cm respectively.

ii. Now, draw the radius OP of the larger circle.

iii. Construct a perpendicular bisector of OP intersecting OP at point O’.

iv. Considering O’P as radius, draw another circle.

v. From point P, draw tangents PQ and PR(can see in the figure)

Justification:By applying Pythagoras theorem, we have;

PQ² = OP² – OQ²

= 6² – 4²

= 36 – 16 = 20

Or, PQ = 2√5 cm