Angle Formed by Tangents and Secants
How to find the angle formed by tangents and secants of a circle: 3 formulas, 3 examples, and their solutions.
Secant
A secant is a line
that passes through a circle
at two points.
FormulaTwo Intersecting Secants
θ = [1/2](m[arc BD] - m[arc AC])
θ: Angle formed by two intersecting secants
arc BD: The outer arc
arc AC: The inner arc
Example
xº: is the angle
formed by two intersecting secants.
The outer arc is 108º.
The inner arc is 44º.
Then x = [1/2](108 - 44).
108 - 44 = 64
[1/2]⋅64 = 32
So x = 32.
Formulaa Tangent and a Secant
θ = [1/2](m[arc BC] - m[arc AC])
θ: Angle formed by a tangent and a secant
arc BC: The outer arc
arc AC: The inner arc
Example
xº: is the angle
formed by a tangent and a secant.
The outer arc is 143º.
The inner arc is 63º.
Then x = [1/2](143 - 63).
143 - 63 = 80
[1/2]⋅80 = 40
So x = 40.
FormulaTwo Intersecting Tangents
θ = [1/2](m[arc ABC] - m[arc AC])
θ: Angle formed by two intersecting tangents
arc ABC: The outer arc
arc AC: The inner arc
Example
See this circle.
Set the outer arc α.
The inner arc is 130º
These two arcs form a circle.
So [α] + [130] = 360.
Move +130 to the right side.
Then α = 230.
Write 230º
next to the outer arc.
xº: is the angle
formed by two intersecting tangents.
The outer arc is 230º.
The inner arc is 130º.
Then x = [1/2](230 - 130).
230 - 130 = 100
[1/2]⋅100 = 50
So x = 50.