SOLUTION: given a circle, draw two chords who's lengths are in the ratio 1:2 and who's distances from the center are in the ration 2:1. Find the length of each chord in terms of the radius '

Question 839555: given a circle, draw two chords who's lengths are in the ratio 1:2 and who's distances from the center are in the ration 2:1. Find the length of each chord in terms of the radius 'r' of the circle. Find their lengths if r = 10 cm.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
given a circle, draw two chords who's lengths are in the ratio 1:2
and who's distances from the center are in the ration 2:1.
Find the length of each chord in terms of the radius 'r' of the circle.
:
A right triangles formed by the chords, with sides: half the chord length,
distance from the center, and the radius, which is the hypotenuse.
:
As I examine these, it's apparent that the two triangles are indentical,
one triangle the distance from the center is the longer side and the other
triangle the long side is half the length of the longer chord.
:
On the right triangle let the shorter leg = 2, the longer leg = 2s
The chord will be twice the length of the legs
Find s in terms of r
s^2 + (2s)^2 = r^2
s^2 + 4s^2 = r^2
5s^2 = r^2
s^2 =
s =
The shorter chord =
The longer chord =
:
"Find their lengths if r = 10 cm."
The shorter chord:
= = 8.94 cm
The longer chord:
= = 17.89 cm

The longer chord =
:

RELATED QUESTIONS
Two perpendicular chords divide a circle with a radius of 13 cm into four parts. If the... (answered by ikleyn)

Two perpendicular chords divide a circle with a radius of 13 inches into four parts. If... (answered by mananth)

In a circle of radius 5cm, there are two parallel chords of lengths 8cm and 6cm... (answered by oscargut)

Two parallel chords lies on opposite sides of a center of a circle of radius 13cm.Their... (answered by ikleyn)

Hi! I need help on a problem my teacher gave me for homework. On the problem, it gives... (answered by ankor@dixie-net.com)

two parallel chords of length 30 cm and 16 cm are draw on the opposite sides of center of (answered by ikleyn)

O IS THE CENTER OF THE CIRCLE. AC AND BC ARE TWO EQUAL CHORDS OF THE CIRCLE. IF ANGLE... (answered by Alan3354)

In the image, point A marks the center of the circle. Which two lengths must form a ratio (answered by ikleyn)