Question

if a line intersects two concentric circles at ABC and D then prove that AB=CD question 10

Answer 1

aloha user!! ☺️

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given: two concentric circles with chords BC and AD.

to prove: AB = CD

construction: draw a perpendicular from the center of the circle to the chord. Join B and O, O and C, O and A & O and D.

( please see attachment )

proof:
In ∆ OBF and ∆ OCF
OB = OC. ( equal radii of circle )
angle OFB = angle OFC. ( each 90° )
OF = OF ( common )

∆ OBF and ∆ OCF are congruent by RHS criteria.
so by CPCT we can write:

BF = FC---------------(1)

similarly in ∆ OAF and ∆ ODF

OF = OF ( common )
angle OFA = angle OFD. ( each 90° )
OA= OD ( radii of same circle )

∆ OAF and ∆ ODF are congruent by RHS criteria.

by CPCT we can write:

AF= FD---------------(2)

subtracting (1) from (2) we get:

AF - BF = FD - FC
AB = CD

$hence \: proved.$
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hope it helps !!

peace out !!

Answer 2

Sorry for the bad handwriting so plz don't mind it but mind my sum.

Hope it helps

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