The given figure shows a circle with centre O. CD and AB are chords of the circle. Chord AB is 6 cm long and is located 4 cm from the centre of the circle.
Which of the following statement isincorrect?
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Chord CD is at a distance of 4 cm from the centre of the circle.
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The radius of the circle is 5 cm.
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The length of chord CD is 6 cm.
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The measure ofAOB is twice that ofCOD.
Ans :
It isknown that perpendicular from the centre of the circle to the chord bisects the chord.
∴CD = 2FC
⇒CD = 2×3 cm = 6 cm
It is given that the length of AB is 6 cm.
It isknown that equal chords subtend equal angles at the centre of the circle.
⇒ AOB =COD
Thus, statementDis incorrect.
The correct answer is D.
- in this question how can we say that radius oss 5 cm ????
In your question figure is missing. But you can follow the method given below,
Let perpendicular from the centre O meets chord AB at point E.
Since the perpendicular from the centre of the circle to the chord bisects the chord. Therefore,
AE = 3 cm And OE = 4 cm
Using Pythagoras Theorem in triangle OAE, we have,
Hence, radius of the circle is 5 cm.
Let perpendicular from the centre O meets chord AB at point E.
Since the perpendicular from the centre of the circle to the chord bisects the chord. Therefore,
AE = 3 cm And OE = 4 cm
Using Pythagoras Theorem in triangle OAE, we have,
Hence, radius of the circle is 5 cm.