Angle Formed by a Tangent and a Chord
How to find the angle formed by a tangent and a chord of a circle: formula, 2 examples, and their solutions.
Formula
Formula
θ = [1/2] m[arc AB]
θ: Angle formed by a tangent and a chord
arc AB: Intercepted arc
Example 1
Example
Solution
xº is the angle
formed by a tangent and the chord AB.
Arc AB is the intercepted arc.
The measure of the arc is 110.
So x = [1/2]⋅110.
[1/2]⋅110 = 55
So 55 is the answer.
Example 2
Example
Solution
80º is the inscribed angle.
The blue arc is the intercepted arc.
Set the measure of the arc α.
Then [1/2]⋅α = 80.
(α is read as [alpha].)
Multiply 2 to both sides.
Then α = 160.
Write 160º
next to the blue arc.
xº is the angle
formed by a tangent and a chord.
The blue arc is the intercepted arc.
The measure of the arc is 160.
So x = [1/2]⋅160.
[1/2]⋅160 = 80
So 80 is the answer.