Question

A circle has radius 26cm and length of it's chord is 48cm.find how far is the chord from the center of the circle?​

Answer 1

To find out how far the chord is from the center of the circle, we can calculate the angle subtended by each arc using the formula angle = (arc length / radius). Using trigonometric ratios, we can then find the distance between the chord and the center of the circle. In this case, the distance is approximately 40.77cm.

Step-by-step explanation:

To find out how far the chord is from the center of the circle, we can use the properties of congruent chords. Since the length of the chord is 48cm, it divides the circle into two congruent arcs. Each arc subtends an angle at the center of the circle. We can calculate this angle using the formula: angle = (arc length / radius). In this case, the arc length is 48cm, and the radius is 26cm. Therefore, the angle subtended by each arc is approximately 1.846 radians.

Now, the chord divides the circle into two congruent triangles. The angle subtended by each arc is also the angle formed between the chord and the radius of the circle. Let's call this angle θ. In each triangle, we have a right angle (formed by the radius and the chord) and angle θ. Using trigonometric ratios, we can find the distance between the chord and the center of the circle. In this case, since we know the length of the chord (48cm) and the angle θ (approximately 1.846 radians), we can use the sine ratio to calculate the distance:

distance = chord * sin(θ)

distance = 48cm * sin(1.846)

distance ≈ 40.77cm

Answer 2

The chord is 10cm from the center of the circle

Step-by-step explanation:

Here, we want to find the distance of the chord from the center of the circle

A line from the center to the chord will

divide the chord into two parts

each will have a measure of 48/2 = 24 cm

So now we have a right/angled triangle with hypotenuse of 26

To find the height, we use Pythagoras’ theorem which states that the sum of the squares of the other sides equal the square of hypotenuse

h ^2 + 24^2 = 26^2

h^2 = (26-24)(26+24)

h^2 = 100

h = square root of 100, which is 10