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  • Write True or False and justify your answer in each of the following: Two chords AB and CD of a circle are each at distances 4 cm from the centre. Then AB equal to CD.

Write True or False and justify your answer in each of the following:  Two chords AB and CD of a circle are each at distances 4 cm from the centre. Then AB = CD.

Answers (1)

Given,

AB & CD are chords of a circle and they are equidistant (4 cm) from the centre O.

To find whether AB = CD

As the two chords AB and CD are each at a distance of 4 cm from the centre, this distance will be perpendicular distance.

Hence OM \perp AB & ON \perp CD

OM = ON = 4 cm

\therefore OM bisects AB & ON bisects CD

i.e., AM = \frac{1}{2} AB \: \: and\: \: DN = \frac{1}{2} DC

\angle OMA = \angleOND = 90°

OA = OD                                 (Both are radius)

\triangleAOM \cong \triangleDON                    (RHS Congruence)

AM = DN                                (by CPCT)

2AM = 2DN                            (Multiplying both sides by 2)

AB = DC

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