Question

Construct a tangent to a circle of radius 4 cm form 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 1: Mark a point O on the paper

Step 2: With O as center and radii 4cm and 6cm, draw two concentric circles.

Step 3: Mark a point P on the outer circle.

Step 4: Join OP.

Step 5: Draw the perpendicular bisector XY of OP, cutting OP at Q.

Step 6: Draw a circle with Q as center and radius OQ (or PQ), to intersect the inner circle in points T and T’.

Step 7: Join PT and PT’.

Here, PT and PT’ are the required tangents.

PT = PT’ 4.5 cm (Approx)

Verification by actual calculation

Join OT to form a right △OTP (Radius is perpendicular to the tangent at the point of contact)

In right  △OTP,

OP² = OT² + PT²   (Pythagoras Theorem)

\(\Rightarrow PT=\sqrt{OP^2-OT^2}\)