A chord of a circle of radius 26cm is 10cm from the centre of the circle . Calculate the length of the chord
Draw the perpendicular from the centre to the chord.
You are now looking at a right-angled triangle with a height of 10
a hypotenuse of 26 and a missing base of x
x^2 + 10^2 = 26^2
find x, and remember that x is only half the chord
To calculate the length of the chord, we need to use a theorem in circle geometry called the Pythagorean Theorem.
The theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the chord acts as the hypotenuse, and the radius of the circle is one of the other sides.
Let's use the variables c for the length of the chord and r for the radius. We also have another side equal to 10 cm, which is the distance from the center of the circle to the chord.
According to the Pythagorean theorem:
c^2 = r^2 + 10^2
Since the radius of the circle is given as 26 cm, we can substitute the values:
c^2 = 26^2 + 10^2
Simplifying the equation:
c^2 = 676 + 100
c^2 = 776
Taking the square root of both sides to find c:
c = √776
c ≈ 27.86 cm
Therefore, the length of the chord is approximately 27.86 cm.
To calculate the length of a chord in a circle, you need the length of the radius and the distance of the chord from the center of the circle.
In this case, we are given that the radius of the circle is 26 cm, and the chord is 10 cm away from the center.
Let's solve it step by step:
Step 1: Draw a diagram of the given information. Draw a circle with the center and radius labeled. Mark the distance of the chord from the center.
Step 2: We can see that the chord, the radius, and the line connecting the center of the circle to the chord form a right triangle.
Step 3: Apply the Pythagorean theorem to find the length of the chord.
The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the radius is the hypotenuse, and the distance from the center to the chord acts as one side of the right triangle. We want to find the length of the chord, which is the other side.
Let's denote the length of the chord as "c," the radius as "r," and the distance from the center to the chord as "d."
According to the Pythagorean Theorem:
c^2 = r^2 - d^2
Substituting the given values:
c^2 = (26 cm)^2 - (10 cm)^2
= 676 cm^2 - 100 cm^2
= 576 cm^2
Now, take the square root of both sides to get the value of "c":
c = √(576 cm^2)
= 24 cm
Therefore, the length of the chord is 24 cm.