Keeping that in mind, we will take a look at the given diagram.
On the diagram we have two perpendicular bisectors. Each of these segments is a part of a diameter by the Perpendicular Chord Bisector Converse. Therefore, these perpendicular bisectors intersect at the center of the circular plate.
Remember that the diameter of a circle is twice as long as its radius. Thus, to determine the diameter of the plate we will find its radius first. Let's mark the radius on the diagram.
We can see that the radius forms a right triangle with legs of 6 inches and 72= 3.5 inches. The radius is the hypotenuse of this triangle. Let r represent the length of the radius. To find the value of r we will use the Pythagorean Theorem.
6^2+ 3.5^2=r^2
Let's solve the above equation for r.
Since r represents a length we only consider positive solutions of the equation. Finally, we can calculate the length of the diameter of the plate to the nearest tenth of an inch.
