Question 6 In figure AB and CD are common tangents to two circles of equal radii. Prove that AB = CD.
Givne AB and CD are tangents to two circle of equal radii To prove AB =CD
Construction Join OA, OC, O’ B and O’D Proof Now, ∠OAB=90∘ [ Tangents at any point of a circle is perpendicular to radius through the point of contact] Thus, AC is a straight line Also. ∠OAB+∠OCD=180∘ ∴AB∥CD Similarly, BD is straight line And ∠O′BA=∠O′DC=90∘ Also, AC = BD [ radii of two circles are equal] In quadrilateral ABCD. ∠A=∠B=∠C=∠D=90∘ And AC =BD Hence. AB=CD [ opposite sides of rectangle are equal]