the length of a chord of a circle of radius 10cm is 12cm. find the distance of the chord from the centre of the circle
Answers
Chord AC = 12 cm
AB = 6 cm (Half of chord AC)
AO = 10 cm (Radius)
By Pythagoras theorem,
h² = p² + b²
AO² = OB² + AB²
10² = OB² + 6²
OB² = 100 - 36
OB² = 64
OB = 8 cm
The distance of the chord from the centre of the circle is 8 cm if the length of a chord of a circle of radius 10cm is 12cm
Given:
- A circle
- Radius = 10 cm
- Chord length = 12
To Find:
- Distance of Chord from Center of circle
Solution:
- Assume that O is the center of circle.
- AB is the Chord.
- Join OA and OB
- OA = OB = Radius = 10 cm
- Draw OM ⊥ AB
- OM is the distance of the chord from the centre of the circle
Step 1:
"Perpendicular from center on chord divides the chord in 2 Equal Parts"
Hence AM = MB = AB/2 = 12/2 = 6 cm
Step 2:
Pythagorean theorem:
"Square on the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two perpendicular sides."
ΔAMO is right angle Triangle Hence,
OA² = AM² + OM²
Step 3:
Substitute AM = 6 cm and OA = 10 cm and solve for OM
10² = 6² + OM²
=> 100 = 36 + OM²
=> 64 = OM²
=> OM = ± 8
As length can not be negative
Hence OM = 8 cm
The distance of the chord from the centre of the circle is 8 cm
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