The radius of the circle is 5 cm and distance of the chord from the centre of the circle is 4 cm.
Find the length of the chord.
Answers
Step-by-step explanation:
R = 5 cm, r = 3 cm. d = 4 cm.
☞length of the common chord = ?
• When measured Chord CD = 6 cm.
• Circles with centre A and B, intersect at points C and D.
• CD is common chord.
•Perpendicular bisector of CD is AB. AC = 5cm. BC = 3cm.
∴ Chord, CD= 2 × OC = 2 × 3 ∴ Chord, CD = 6 cm.
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Answer:
In the given circle, radius OA = 5 cm: distance of the chord AB from the centre is 4 cm.
So, seg AM = seg MB (Perpendicular drawn from the centre to a chord bisects the chord)
By using Pythagoras theorem, in right triangle AOM,
AM2 + OM2 = OA2
⇒ AM2 + 42 = 52
⇒ AM2 +16 = 25
⇒ AM2 = 25 – 16
⇒ AM2 = 9
⇒ AM = 3 cm
But seg AM = seg MB = 3 cm
∴ Seg AB = seg AM + seg MB = 3 cm + 3 cm = 6 cm
Therefore, the length of the chord is 6 cm.