Question

6. Prove that a tangent line to a circle is perpendicular to a radius of that circle at the point of tangency. (This is the converse of the result proved by contradiction on page 93.)

Answer 1

Given AB is the tangent at p of the circle centred at o and op is the radius passing through pe Harce to prove: AB is perpendicular to op.

construc on? Let us consider a point o on the tangent AB. Joining o anda. proof! Encept p, all other points dying on the rangeant AB is situated outside the circle . iod will intersect the circle at a point, Let the point be R. - ORLoa [since R die between 0 ando Again ORFOPſ Radius of same circler an op Log since & is an arbitrary point on the tangent AB, so that op is the smallest among the segment joining the point o to any point on the tangent AB. Again smallest distance is the perpendia cular distance. - AB is berpendicular to op.