A chord of length 16 cm is drawn in a circle of radius 10 cm. Find the distance of the chord from the centre of the circle.
Answers
Answer:
the distance between chord from the centre is 6 cm
The distance of the chord of length 16 cm from the centre of the circle is 6 cm.
Step-by-step explanation:
The length of the chord, AB = 16 cm
The radius of the circle, OA = 10 cm
Let the centre of the circle be "O", the perpendicular distance be “ON” (as shown in the figure attached below)
We know that the perpendicular drawn from the centre of the circle to its any chord always bisects the chord.
∴ AN = ½ AB = ½ * 16 = 8 cm
In right ∆AON, applying Pythagoras theorem, we get
AO² = ON² + AN²
⇒ ON² = AO² – AN²
⇒ ON² = 10² – 8²
⇒ ON = √[100 - 64]
⇒ ON = √36
⇒ ON = 6 cm
Thus, the distance of the chord from the centre of the circle is 6 cm.
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