# Segments Formed by a Tangent and a Secant

How to find the segments formed by a tangent and a secant of a circle: formula, 1 example, and its solution.

## Formula

### Formula

Ray PA and PC

are the tangent and the secant

that start from the same point P.

Then three segments are formed:

PA, PB, and BC.

Then PA^{2} = PB⋅PC.

## Example

### Example

### Solution

x, 4, and 5

are the segments

formed by a tangent an a secant.

Then x^{2} = 4(4 + 5).

4 + 5 = 9

4⋅9 = 36

x^{2} = 36

Square root both sides.

Then x = √36.

x is a line segment.

So x is plus.

So you don't have to write ± sign.

Quadratic Equation: Square Root

36 = 6^{2}

√6^{2} = 6

So x = 6.