In Figure 1, common tangents AB and CD to the two circles with centres 01and 02 intersect at E. Prove that AB = CD.
Given: AB and CD are common tangents to both the circles.
To prove: AB = CD
We know that two tangents drawn to a circle for the same exterior point are
Thus we get
AE = EC (i)
ED = EB (ii)
AB = AE + EB (iii)
CD = CE + ED (iv)
AB = EC + EB from (i) and (iii)
CD = EC + EB from (ii) and (iv)
Therefore AB = CD
Concept: Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
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