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The points (0, 3) and (3, 0) lie on the circle in the figure above and
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08 Dec 2022, 12:18
08 Dec 2022, 12:18
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The points (0, 3) and (3, 0) lie on the circle in the figure above and the base of the inscribed isosceles triangle passes through the center of the circle. What is the area of the triangle?
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Re: The points (0, 3) and (3, 0) lie on the circle in the figure above and
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11 Dec 2022, 04:00
11 Dec 2022, 04:00
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The circle touches (0, 3) and (3, 0), so its center must be at (3, 3) and its radius must be 3. Since the base of triangle passes through the center of the circle, the base of the triangle must be the diameter of length 6. Given the triangle is isosceles and inscribed within the circle, a line from the circle’s center to the triangle’s corner equals the triangle’s height. This height must be the radius of the circle. The area of a triangle is 0.5 × base × height: 0.5 × 6 × 3 = 9.
The circle touches (0, 3) and (3, 0), so its center must be at (3, 3) and its radius must be 3. Since the base of triangle passes through the center of the circle, the base of the triangle must be the diameter of length 6. Given the triangle is isosceles and inscribed within the circle, a line from the circle’s center to the triangle’s corner equals the triangle’s height. This height must be the radius of the circle. The area of a triangle is 0.5 × base × height: 0.5 × 6 × 3 = 9.
Re: The points (0, 3) and (3, 0) lie on the circle in the figure above and
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03 Sep 2024, 11:18
03 Sep 2024, 11:18
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