Two parallel chords lie on opposite sides of the centre of a circle of radius 13cm.their lengths are 10cm and 24cm.what is the distance between the chords?
17
17cm
Well, try to get the distance from the center of the circle to the center of one of the chords
For example the 10 cm chord.
line from circle center to middle of 10 cm chord hits chord at right angle, cuts it into two 5 cm legs
now have right triangle with leg 5 and hypotenuse 13 so other leg is sqrt(169-25)
or 12
so 12 is distance from center to the 10 cm chord.
Now do the distance to the 24 cm chord and add the two distances.
please give me answer
To find the distance between the chords, we need to find the distance from the center of the circle to each chord.
Given that the radius of the circle is 13 cm, the distance from the center of the circle to each chord is equal to the radius.
Let's call the distance between the chords "d".
Now, let's draw a line from the center of the circle perpendicular to each chord.
This line will be the height of a right triangle, with the radius as the hypotenuse and the distance "d" as one of the legs.
Using the Pythagorean theorem, we have:
d^2 + (10/2)^2 = 13^2 (since the length of one chord is 10 cm, the half of it is 10/2 = 5 cm)
d^2 + 25 = 169
d^2 = 144
d = √144
d = 12 cm
Therefore, the distance between the chords is 12 cm.