Draw a circle with centre C and radius 3 cm. Take point P such that CP = 7 cm and draw tangents from P. Measure the tangent segments and verify by calculation.

Answer: Two tangents PA and PB, each about 6.3 cm.

Steps of construction:

1. Draw a circle with centre C and radius 3 cm.
2. Take point P such that CP = 7 cm and draw seg CP.
3. Draw the perpendicular bisector of seg CP; let it cut CP at M, the midpoint of CP.
4. With M as centre and radius MC (= 3.5 cm), draw a circle. It cuts the given circle at points A and B.
5. Draw lines PA and PB. These are the required tangents.

[Figure: circle with centre C, radius 3 cm; external point P, CP = 7 cm; auxiliary circle on diameter CP with centre M; tangents PA and PB touching at A and B.]

Why it works: A and B lie on the circle with diameter CP, so \(\angle CAP = \angle CBP = 90^\circ\) (angle in a semicircle). A line perpendicular to a radius at its outer end is a tangent.

Check: each tangent segment should measure \(\sqrt{7^2 - 3^2} \approx 6.3\) cm, and PA = PB.