Question

AB and CD are two chords such that AB = CD. If
chord AB subtend an angle of 45° at the centre of
the circle, then find the angle subtended by chord
CD at the centre of the circle.
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Answer 1

Step-by-step explanation:

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9th

Maths

Circles

Perpendicular to a Chord through the Centre

O is the centre of the circ...

MATHS

O is the centre of the circle. AB and CD are two chords of the circle. OM⊥AB and ON⊥CD. If OM=ON=2 cm and AM=BM=4.5 cm, then CD is equal to

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ANSWER

Given- AB and CD are two chords of a circle with centre O.

OM⊥AB and ON⊥CD

AM=AN=4.5 cm

OM=ON=2 cm

Solution-

AM=AN=4.5 cm

∴AB=AM+AN=(4.5+4.5) cm =9 cm

OM and ON are the perpendicular distances of AB and CD respectively.

Since OM⊥AB and ON⊥CD

Now OM=ON=2 cm

∴AB and CD are equidistant from O.

∴AB=CD

Since chords of a circle, which are equidistant from the centre of the same circle are equal in length.

∴AB=CD=9 cm

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