two parallel chords lie on opposite sides of the centre of a circle of radius 13cm.thir lengths are 1ocm and 24cm.what is the distance between the chords
draw lines from the centre to the midpoints of the two chords.
You will have two right-angled triangles,
one with sides x, 5, 13
the other with sides, y, 12, 13
Use Pythagoras to find x=12, and y=5
so the distance between them is
12+5 or 17 cm
Answer
To find the distance between the parallel chords, we need to find the distance between the center of the circle and one of the chords.
Let's call the distance between the center of the circle and the chord with a length of 10 cm as D10, and the distance between the center and the chord with a length of 24 cm as D24.
In a circle, the perpendicular distance from the center to a chord bisects the chord. This means that the distance from the center to the chord with a length of 10 cm divides it into two equal parts, each measuring 5 cm. Similarly, the distance from the center to the chord with a length of 24 cm divides it into two equal parts, each measuring 12 cm.
Now, we can form a right triangle with the radius of the circle (13 cm), half of the chord lengths (5 cm and 12 cm), and the distance between the center of the circle and the chords (D10 and D24).
Using the Pythagorean theorem, we can calculate the distances:
For the chord with a length of 10 cm:
D10^2 = (13 cm)^2 - (5 cm)^2
D10^2 = 169 cm^2 - 25 cm^2
D10^2 = 144 cm^2
D10 = 12 cm
For the chord with a length of 24 cm:
D24^2 = (13 cm)^2 - (12 cm)^2
D24^2 = 169 cm^2 - 144 cm^2
D24^2 = 25 cm^2
D24 = 5 cm
Finally, to find the distance between the two parallel chords, we subtract the lengths of the two distances:
Distance between the chords = D10 - D24
Distance between the chords = 12 cm - 5 cm
Distance between the chords = 7 cm
Therefore, the distance between the two parallel chords is 7 cm.
To find the distance between the parallel chords, we need to use the properties of a circle. Here's how you can calculate it:
Step 1: Draw a line from the center of the circle perpendicular to the chords. This line will bisect both chords.
Step 2: The distance from the center of the circle to each chord is half of their lengths. Therefore, the distance from the center to the chord with a length of 10 cm is 10/2 = 5 cm, and the distance to the chord with a length of 24 cm is 24/2 = 12 cm.
Step 3: Now, you have a right-angled triangle formed by the radius of the circle, the perpendicular line from the center to the chords, and half the length of the chords.
Step 4: Apply the Pythagorean theorem to find the distance between the parallel chords. The formula is a^2 + b^2 = c^2, where "a" and "b" are the two legs (5 cm and 12 cm) of the right triangle, and "c" is the hypotenuse, the distance between the chords.
Using the Pythagorean theorem, we have:
5^2 + 12^2 = c^2
25 + 144 = c^2
169 = c^2
Taking the square root of both sides, we find:
c = √169
c = 13 cm
Therefore, the distance between the two parallel chords is 13 cm.