Remember that in a circle two minor arcs are congruent if and only if their corresponding chords are congruent.
Each arc has a measure of 90^(∘) and each chord is approximately 2.12 feet.
Practice makes perfect
We are given that Roberto is designing a logo. In his project each chord is equal in length. Let's take a look at the simplified diagram.
Now let's recall that in a circle two minor arcs are congruent if and only if their corresponding chords are congruent. For our exercise this means that all four arcs have the same measure. Let's call it x.
To find the measure of one arc we will use the fact that the whole circle has a measure of 360^(∘). Therefore the sum of four times x will be equal to 360.
The measure of each arc is 90^(∘). Let's add this information to our diagram.
Next, if we connect the opposite vertices of the quadrilateral with segments we will have four congruent isoscelesright triangles. Each of these triangles will have the legs of one half of the diameter of a circle.
If we call the length of the chord s, then we can write an equation using the Pythagorean Theorem. According to this theorem the sum of the squared legs of a right triangle is equal to its squared hypotenuse.
s^2=1.5^2+1.5^2
Let's solve above equation. Notice that since s represents the side length we will consider only the positive case when taking a square root of s^2.
