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 PA2 = PB⋅PC.

Example

Example

Solution

x, 4, and 5
are the segments
formed by a tangent an a secant.

Then x2 = 4(4 + 5).

4 + 5 = 9

4⋅9 = 36

x2 = 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 = 62

62 = 6

So x = 6.