Two parallel chords in a circle of radius 7.5cm measure 12cm and 9cm. They are on the same side of the circle. What is the distance between them?

Guest Jul 3, 2015

#1**+10 **

Here's one method.....but.....maybe not the fastest one !!!

Let the center of the circle lie at the origin and let both chords be parallel to the x axis.

The equation of the circle is x^2 + y^2 = 56.25

The chord of 12 cm in length will have one of its endpoints at (6,y_{1})......and y_{1} =

√[56.25 - 6^2] = √[56.25 -36 ] = 4.5 { taking the positive value of the root }

And

The chord of 9 cm in length will have one of its endpoints at (4.5, y_{2})......and y_{2} =

√[56.25 - 4.5^2] = √[56.25 - 20.25 ] = 6 {again, taking the positive value of the root}

So....the distance between the chords is y_{2} - y_{1} = 6 - 4.5 = 1.5 cm

Here's a pic.....

Note that ED = 9, CB = 12 and FG = 1.5

CPhill
Jul 3, 2015

#1**+10 **

Best Answer

Here's one method.....but.....maybe not the fastest one !!!

Let the center of the circle lie at the origin and let both chords be parallel to the x axis.

The equation of the circle is x^2 + y^2 = 56.25

The chord of 12 cm in length will have one of its endpoints at (6,y_{1})......and y_{1} =

√[56.25 - 6^2] = √[56.25 -36 ] = 4.5 { taking the positive value of the root }

And

The chord of 9 cm in length will have one of its endpoints at (4.5, y_{2})......and y_{2} =

√[56.25 - 4.5^2] = √[56.25 - 20.25 ] = 6 {again, taking the positive value of the root}

So....the distance between the chords is y_{2} - y_{1} = 6 - 4.5 = 1.5 cm

Here's a pic.....

Note that ED = 9, CB = 12 and FG = 1.5

CPhill
Jul 3, 2015