Question

Draw a line AB = 6 cm. Construct a circle with AB as diameter. Mark a point P at a distance of 5 cm from the mid-point of AB. Construct two tangents from P to the circle with AB as diameter. Measure the length of each tangent.

Answer 1

The length of each tangent (PQ or PR) measures 4 cm when constructed and measured accurately, which can also be verified using the Pythagorean theorem:

PQ = `sqrt(OP^2 − OQ^2)`

PQ = `sqrt(5^2 − 3^2)`

PQ = `sqrt(25 − 9)`

PQ = `sqrt16`

PQ = 4 cm