The length of an arc of a circle is the product of the measure of the arc divided by 360 and the circumference of the circle.
length of AB=mAB/360 * 2Ï€ r
Therefore, to find the length of the desired arc, we first need to find its measure. For simplicity, let's label the endpoints of the involved arcs.
Looking at the diagram, we can see that the desired ACD is formed by the adjacent arcs AB and the semicircle BCD.
By the Arc Addition Postulate, we know that the m ACD is the sum of the measures of these two adjacent arcs.
m ACD=m AB+mBCD
From the diagram, we know that m AB is 45^(∘). Also, note that BCD is a semicircle, therefore, its measure is 180^(∘). Let's substitute this value in the above equation, and solve for m ACD.
