PROBLEM:
As illustrated on the figure at the right, the legs of the inscribed right triangle measure 8 cm and 15 cm respectively. What is the measure of the diameter of the circle?
SOLUTION:
• Since the inscribed triangle is right one, to solve for the value of the unknown side, we will use the Pythagorean Theorem.
• Pythagorean Theorem tells us that the area of the square of the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
• The value of c is for the hypotenuse while we'll let a be 8 cm and b for 15 cm.
[tex]\blue {\overline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: }} [/tex]
[tex]\begin{gathered} \large \begin{array}{l} \tt c {}^{2} = a {}^{2} + b {}^{2} \\ \tt c {}^{2} = (8 \: cm) {}^{2} + (15\: cm) {}^{2} \\ \tt c {}^{2} = 64 \: cm {}^{2} + 225 \: cm {}^{2} \\ \tt c {}^{2} = 289 \: cm {}^{2} \\ \tt \sqrt{c {}^{2} } = \sqrt{289 \: cm {}^{2} } \\ \tt c = 17 \: cm\end{array}\end{gathered} [/tex]
[tex]\blue {\overline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: }} [/tex]
• The square root of 289 results to a positive and negative integer of 17 but since we're talking about lengths, we will disregard the negative one.
• The hypotenuse of the inscribed right triangle serves as the diameter of the given circle. Thus, if the measure of the hypotenuse is 17 cm, then the length of the diameter is also 17 cm.
ANSWER:
The measure of the diameter of the circle is 17 centimeters.
