Circle geo q (1 Viewer)

[Joshmosh2]

Find the length of the common chord of two intersecting lines whose radii are 15cm and 13cm and whose centres are 14cm apart.

So I drew up the diagram, with the chord creating two right angled triangles
I labelled one side x, and the other 14-x to find half of the length of the chord

Here's the problem
Only one way of labelling the sides works. If you give the 15, the x^2 counterpart, and the 13 the (14-x) counterpart, you get the answers wrong
However, labelling the 15 with (14-x) and the 13 with the remainder works.
Why is this so?
Is it because you are assuming x is longer than the 14-x bit?
WHY???

 

[Ikki]

Not exactly sure what you're doing but this is how i did it.
Connect radii to the ends of the chord and connecting the centers together creating essentially 4 right angled triangles as you said it was. (Radii from center bisects the chord) which means if u find the chord is divided in half exactly. To find the half, take an angle, say between the radii 13 and the line connecting the chords.
Use cosine rule in the BIG triangle to find that angle and you get Cos A = 5/13
If that is a right angled triangle then the trig ratio fits your triangle as the hypotenuse is 13. Therefore using pythagorus you get the top half to be 12cm. Multiply by 2 to get the full length = 24cm