math help!?

Question

there is a circle with a center point which is named K. line AB has endpoints on the circle.Construct a line through point K that is perpendicular to line AB. Prove that the line you constructed bisects line AB

Answer 1

Let's five a name to the point where your line goes through AB -- call it C.

Now look at the triangles ACK and BCK. Note that they have side KC in common. Note that side AK and side BK have the same length -- which is equal to the radius of the circle. This is because both points are on the circle, and all points on a circle are equidistant from the center.

The next thing to note is that the triangles are both right triangles. The fact that the line KC is perpindicular to AB means that the angle formed is a right triangle.

This means that we can use the Pythagoran theorem.

Len(AC)^2 + Len(KC)^2 = Len(KA)^2

and

Len(BC)^2 + Len(KC)^2 = Len(KB)^2

Since Len(KB) = Len(KC) we must have

Len(AC)^2 = Len(BC)^2 which means that

Len(AC) = Len(BC)

This implies that the line AC is bisected.

Answer 2

It's an isoceles trangle divided into two right triangles

Answer 3

Ew geometry. Can't help you there.