Question: A right triangle is inscribed in a circle. The legs of the triangle have lengths 6 and 8. What is the diameter of the circle?
(A) 8
(B) 8π
(C) 9√3
(D) 10
(E) 12
“A right triangle is inscribed in a circle. The legs of the triangle''- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. GMAT quant section analyses the logical aptitude and analytical knowledge of the candidates. The candidates must select the correct option by estimating the problems utilising proper rules of mathematics. The candidates must know basic calculations of mathematics to solve GMAT Problem Solving questions. The mathematical problems of the GMAT Quant topic in the problem-solving part can be solved with better skills in mathematical calculations. The candidates can practice questions by answering from the book “The Official Guide for GMAT Review”.
Solution and Explanation:
Approach Solution 1:
The problem statement informs that:
Given:
- A right triangle is inscribed in a circle
- The legs of the triangle have lengths 6 and 8
Find Out
- the diameter of the circle
Since a right triangle is inscribed in a circle, the diameter of the circle= hypotenuse of the triangle.
According to Pythagoras' theorem,
Hypotenuse^2= 6^2 + 8^2
=36 + 64
=100
Hypotenuse= 10
Therefore, the diameter of the circle = 10
Correct Answer: (D)
Approach Solution 2:
The problem statement suggests that:
Given:
- A right triangle is inscribed in a circle
- The legs of the triangle have lengths 6 and 8
Find Out
- the diameter of the circle
As per the theorem of a right triangle inscribed in a circle,
an angle when created from the diameter of the circle, it is considered as a right triangle.
Or, it can be stated as when a right triangle is inscribed in a circle, the longest side of the triangle is the diameter of the circle.
Therefore, diameter of the circle = (6^2+8^2)^1/2= 10
Correct Answer: (D)
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