Question: What is the circumradius of a triangle with sides 5, 12, and 13?
Options:
6.5
7
8
9
Correct Answer: 7
Solution:
For a right triangle, the circumradius R = hypotenuse/2 = 13/2 = 6.5.
What is the circumradius of a triangle with sides 5, 12, and 13?
Practice Questions
Q1
What is the circumradius of a triangle with sides 5, 12, and 13?
6.5
7
8
9
Questions & Step-by-Step Solutions
What is the circumradius of a triangle with sides 5, 12, and 13?
Correct Answer: 6.5
Step 1: Identify the sides of the triangle. The sides are 5, 12, and 13.
Step 2: Check if the triangle is a right triangle. A triangle is a right triangle if the square of the longest side (hypotenuse) equals the sum of the squares of the other two sides.
Step 3: Calculate the squares of the sides: 5^2 = 25, 12^2 = 144, and 13^2 = 169.
Step 4: Check if 5^2 + 12^2 equals 13^2: 25 + 144 = 169, which is true.
Step 5: Since the triangle is a right triangle, use the formula for the circumradius R = hypotenuse / 2.
Step 6: Substitute the hypotenuse (13) into the formula: R = 13 / 2.
Step 7: Calculate R: 13 / 2 = 6.5.
Circumradius of a Triangle – The circumradius is the radius of the circumcircle, which is the circle that passes through all the vertices of the triangle. For a right triangle, it can be calculated as half of the length of the hypotenuse.
Properties of Right Triangles – In a right triangle, the side opposite the right angle is the hypotenuse, and the circumradius can be derived directly from this property.
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