Question

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.

Answer 1

Steps of Construction:
Step I: Take a point O and draw a circle of radius OA = 4 cm. Also, draw a concentric circle of radius OB = 6 cm

Step II: Find the mid-point C of OB and draw a circle of radius OC = BC. Suppose this circle intersects the circle of radius 4 cm at P and Q.
Step III: Join BP and BQ to get the desired tangents from a point B on the circle of radius 4 cm. By actual measurement, we find BP = BQ = 4.5 cm.

Justification:
In ∆BPO, we have