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Question 6
In figure AB and CD are common tangents to two circles of equal radii. Prove that AB = CD.


Solution

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
ABCD
Similarly, BD is straight line      
And OBA=ODC=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]

Mathematics

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