MATHEMATICS · Multi-part · GCSE · Mathematics · Geometry and Measures · Geometry and Measures
Problem
You are given a circle with centre O and radius 4 cm. A point P is located such that OP=7 cm. Using only a ruler and compass, construct the tangents from P to the circle and answer the following:
(i) Write the complete step-by-step construction procedure.
(ii) After completing the construction, label the points of contact as T1 and T2. Prove that the two lines PT1 and PT2 you have drawn are tangents to the circle.
(iii) Prove that the lengths of the two tangent segments are equal, that is, PT1=PT2.