A triangle with sides measuring 8, 15 and 17 units is inscribed in a circle. What is the radius of the circle, in units?
1 answer:
Answer: radius of the circle is 8.5 units
Step-by-step explanation:
The diagram of the circle and the inscribed triangle is shown in the attached photo. Looking at the length of each side of the triangle given, the lengths form a Pythagorean triple. We can confirm by applying Pythagoras theorem
Hypotenuse^2 = opposite side^2 + adjacent^2. It becomes
17^2 = 8^2 + ``15^2
289 = 64 + 225
289 = 289
This means that the triangle formed is a right angle triangle.
According to Thales theorem,
The diameter of the circle always subtends a right angle to any point on the circle. Since the diameter is the longest side of the circle and the angles is formed on a point on the circle,
Diameter = 17
Radius = diameter/2 = 17/2 = 8.5
You might be interested in