Question

VX is a perpendicular bisector of chord ZC. Find the length of the diameter VX.

Answer 1

In this case, we can identify two similar triangles like this:

Since VX is a bisector of ZC it cuts ZC into two equal-length segments, then ZY and YC have the same length and we can formulate the following expression:

ZY = YC

ZY = 18

Since we are dealing with similar triangles, we can formulate the following expressions for VYZ and ZYX:

`(VY)/(ZY)=(ZY)/(XY)`

By replacing 18 for ZY and 27 for XY, we get:

`(VY)/(18)=(18)/(27)`

By multiplying both sides by 18, we can solve for 18, to get:

`VY=(18)/(27)*18=12`

By adding the length of VY to the length of XY, we get:

VY + XY = 12 + 27 = 39

Adding VY to XY we should get VX, which is the diameter of the circle. Then VX = 39