In a circle of radius 10 centimetres, find the distance of a chord of length 12 centimetres
Answers
Answer:
here it is
Step-by-step explanation:
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Chord of the circle = 12 cm. Half the chord length = 6 cm. Radius of the circle = 10 cm. Distance of the midpoint of the chord from the centre of the circle = [10^2–6^2]^0.5 = [100–36]^0.5 = 64^0.5 = 8 cm.
⇒ Given:
→ Length of radius = 10 cm
→ Length of the chord = 12 cm
⇒ To Find:
→ The distance between the chord and the centre of the circle.
⇒ Formula to use:
→ The Pythagoras theorem:
Altitude² + Base² = Hypotenuse²
⇒ Solution:
Please refer the attachment for diagrammatical representation.
In this figure:
OA is the radius. [r]
AC is the chord. [c]
OB is the distance of the chord from the center. [x]
We also know that the segment OB when extended, bisects the chord.
In this figure, we can see that a ΔAOB is formed.
Here, putting the values we know:
OA = 10 cm
AB = 6 cm [half of the chord]
OB = x
As a right angled triangle is formed, we can apply the Pythagoras theorem:
Altitude² + Base² = Hypotenuse²
OA² = AB² + OB²
10² = 6² + OB²
100 = 36 + OB²
100 - 36 = OB²
OB² = 64
OB = √64
OB = 8 cm
Hence the distance between the chord and the center is 8 cm.
Knowledge Bytes:
→ Terms Used:
✳Circle
A circle is a closed 2D figure made up of infinite points. Its area is πr² and its perimeter is 2πr.
✳ Radius
The line segment that connects the centre of the circle to the any part in the boundary of the circle is known as radius.
✳ Chord
A chord is the long line segment that connects two points in the curved part of the circle.
