two parallel chord lie in opposite sides of the centre of a circle of radius 13cm. their lengths are 10cm and 24cm.what is the distance between the chord.
Draw radii bisecting both chords.
Draw radii to the ends of the chords.
Now you have right triangles with the hypotenuse equal to the radius.
All the triangles are 5-12-13
So, do the math...
13 cm
To find the distance between the two parallel chords in a circle, you can use the following steps:
Step 1: Draw a diagram and label the given information. The two parallel chords should be drawn on opposite sides of the center of the circle. Label the lengths of the chords as 10 cm and 24 cm.
Step 2: Draw radii from the center of the circle to the endpoints of each chord. These radii will be perpendicular to the chords and will divide them into two equal parts.
Step 3: Since the radii are perpendicular to the chords, they will form right triangles with the chords as their bases. Label the distances from the center of the circle to the chords as h1 and h2.
Step 4: The length of each chord can be expressed as the sum of the two parts created by the radii. Therefore, for the chord with a length of 10 cm, each part will have a length of 10/2 = 5 cm. Similarly, for the chord with a length of 24 cm, each part will have a length of 24/2 = 12 cm.
Step 5: Recognize that you now have two right triangles. In each triangle, you know the length of one side (the radius) and one of the sides adjacent to the right angle (half of the chord length). You need to find the length of the remaining side, which is the distance between the two chords.
Step 6: Use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
In the first right triangle (chord length = 10 cm), you have the following equation:
(13)^2 = (h1)^2 + (5)^2
Simplify the equation:
169 = (h1)^2 + 25
Rearrange the equation to solve for h1:
(h1)^2 = 169 - 25
(h1)^2 = 144
h1 = 12
Repeat the same steps for the second right triangle (chord length = 24 cm):
(13)^2 = (h2)^2 + (12)^2
(h2)^2 = 169 - 144
(h2)^2 = 25
h2 = 5
Step 7: Finally, calculate the distance between the two chords by finding the difference between h1 and h2:
Distance between the chords = h1 - h2
Distance between the chords = 12 - 5
Distance between the chords = 7 cm
Therefore, the distance between the two parallel chords is 7 cm.