Question

If a line intersects two concentric circles with centre O at A,B,C & D,then prove that AB=CD ​

Answer 1

Step-by-step explanation:

Join points O with B, A, C,D

Let the mid point of line BC = E

Join points O and E

In triangle OBE and triangle OEC,

1) OE=OE(Common)

2)OB=OC( Radii of the same circle)

3)BE=EC( Since E is the mid point of line BC)

Therefore, triangle OBE is congruent to triangle OEC

In triangle OAE and triangle OED

1)OE=OE( Common)

2)OA=OD( Radii of the same circle)

3) AE = ED( Since E is the mid point of AD)

Therefore triangle OAE is congruent to triangle OED

AB+BE=EC+CD

AB+BE=BE+CD(Since BE=CE)

Therefore AB=CD

PROVED