Question

There are two concentric circles with centre o ad is a chord of a larger circle intersecting the smaller circle at b and c prove that ab=cd

Answer 1

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Answer 2

Step-by-step explanation:

In two concentric circle with centre 'O'.

AD

is the chord of the bigger circle.

AD

intersect the smaller circle at B and C.

Construction: Draw

OE

perpendicular to

AD

Proof: AD is the chord of the bigger circle with centre 'O' and OE is perpendicular to AD .

∵ OE bisects AD (The perpendicular from the centre of a circle to a chord bisect it)

∴AE=ED ....(i)

BC is the chord of the smaller circle with centre 'O' and OE is perpendicular to AD.

∵

OE bisects BC (from the same theorem)

∴BE=CE .... (ii)

Subtracting the equation (ii) from (i), we get

AE−BE=ED−EC

AB=CD