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In the figure above, rectangle ABCD is inscribed in the circle with center O. What is the area of the circle?
- a)26π
- b)121π
- c)144π
- d)169π
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
In the figure above, rectangle ABCD is inscribed in the circle with ce...
Since ABCD is a rectangle, we can find the length of its diagonal using the Pythagorean Theorem: 102 + 242 = d2. Even better, we can notice that the two legs are in a 5:12 ratio, and therefore triangle BCD is a 5-12-13 triangle. In either case, we find that DB = 26. Since DB is also a diameter of the circle, the radius of the circle is 26/2 = 13, and therefore, the area of the circle is πr2 = π(13)2 = 169π.
Most Upvoted Answer
In the figure above, rectangle ABCD is inscribed in the circle with ce...
Since ABCD is a rectangle, we can find the length of its diagonal using the Pythagorean Theorem: 102 + 242 = d2. Even better, we can notice that the two legs are in a 5:12 ratio, and therefore triangle BCD is a 5-12-13 triangle. In either case, we find that DB = 26. Since DB is also a diameter of the circle, the radius of the circle is 26/2 = 13, and therefore, the area of the circle is πr2 = π(13)2 = 169π.
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In the figure above, rectangle ABCD is inscribed in the circle with center O. What is the area of the circle?a)26πb)121πc)144πd)169πCorrect answer is option 'D'. Can you explain this answer?
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