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l is a line which intersects two concentric circles with common centre o at A,B,C and D . prove that AB=CD.
Asked by surender0145 | 07 Jan, 2024, 08:59: AM

Figure shows the two concentric circles with common centre O.

Common chord AD is intersecting the circles at A, B , C and D .

Let us draw a perpendicular line OE to the common chord as shown in figure.

Right triangles OAE and ODE are congruent because hypotenuses OA and OD are equal ( radii of outer circle )

and OE is common side. hence we get

AE = DE

Right triangles OBE and OCE are congruent because hypotenuses OB and OC are equal ( radii of inner circle )

and OE is common side. hence we get

BE = CE

AE-BE = DE-CE

AB = CD

Answered by Thiyagarajan K | 07 Jan, 2024, 10:42: AM
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