E.g.3 In the following diagram, O is the centre of the circle. <OXY = 30°, <XOY = 60° and XZ = 32 cm. Find XY.

It's quite obvious in this example that XY = XZ / 2. Assume that you draw a line from O to Z, call it OZ. Then OZ and OX are both radii and must thus have the same length. OZ also forms a triangle with OY and YZ (OYZ) that is equal to OXY. This is clear since they both share the side OY and they both have hypotenuses of equal length. Therefore the third side of each triangle must also be equal (in right triangles). From this follows that XY = YZ and that XY + YZ = 32 making XY = 32/2=16. Meow!

E.g.3 In the following diagram, O is the centre of the circle. <OXY = 30°, <XOY = 60° and XZ = 32 cm. Find XY. ​

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E.g.3 In the following diagram, O is the centre of the circle. <OXY = 30°, <XOY = 60° and XZ = 32 cm. Find XY.