Two arc measures are known. Find one of the remaining two.
Value of x: 11 Chord Length: 31
Consider the given diagram.
In the right circle the chord divides the circumference into two arcs. The major arc has a measure of 284^(∘) and the minor arc we have denoted B^(∘). Note that the arcs are adjacent arcs. Let's recall the Arc Addition Postulate.
Arc Addition Postulate
The measure of the arc formed by two adjacent arcs is the sum of the measures of the two arcs.
Since the arc formed by these two adjacent arcs is a circumference, the sum of their arc measures is 360.
284+ B=360
⇕
B = 76
We notice that the minor arc in both circles have the same measure, and we know that the circles are congruent. For congruent arcs in congruent circles the corresponding chords are congruent.
We can write an equation using that the chords have the same length.
3x-2=2x+9
Let's solve this equation.
