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.