Segments Formed by Two Chords

How to find the segments formed by two intersecting chords of a circle: formula, 1 example, and its solution.

Formula

Formula

AB and CD are the chords of a circle
that intersect at point P.

Then four segments are formed:
AP, PB, CP, and PD.

Then AP⋅PB = CP⋅PD.

Multiply the same chord segments.

Example

Example

Solution

x, 4, 3, and 8
are the segments
formed by two intersecting chords.

So x⋅4 = 3⋅8.

Divide both sides by 4.

Then x = 3⋅2.

3⋅2 = 6

So x = 6.