4. Radius of a circle with centre O is 41 units. Length of a chord PQ is 80 units, find
the distance of the chord from the centre of the circle.
Answers
Given,
Length of the chord = 80 units
Radius of the circle = 41 units
To find,
The distance of the chord from the centre of the circle.
Solution,
We can easily solve this mathematical problem by using the following process.
If we take the perpendicular height between the centre of the circle and the midpoint of the chord, as the height of a right angled triangle, then half of the chord will be the height of that right angled triangle and the radius will be the hypotenuse of that right angled triangle.
Base = Half of chord = (80/2) = 40 units.
Hypotenuse = 41 units
Height = Let, x units
According to the data Pythagoras theorem,
(x)² + (40)² = (41)²
x² + 1600 = 1681
x² = 81
x = 9
Hence, the distance of the chord from the centre of the circle is 9 units.
Answer:
Step-by-step explanation:
Length of the chord = 80 units
Radius of the circle = 41 units
To find,
The distance of the chord from the centre of the circle.
Solution,
We can easily solve this mathematical problem by using the following process.
If we take the perpendicular height between the centre of the circle and the midpoint of the chord, as the height of a right angled triangle, then half of the chord will be the height of that right angled triangle and the radius will be the hypotenuse of that right angled triangle.
Base = Half of chord = (80/2) = 40 units.
Hypotenuse = 41 units
Height = Let, x units
According to the data Pythagoras theorem,
(x)² + (40)² = (41)²
x² + 1600 = 1681
x² = 81
x = 9
Hence, the distance of the chord from the centre of the circle is 9 units.