A triangle is drawn with its vertices on the circle C such that one of its sides is a diameter of C and the other two sides have their lengths in the ratio a:b. If the radius of the circle is r, then the area of the triangle is:
Question:
A triangle is drawn with its vertices on the circle C such that one of its sides is a diameter of C and the other two sides have their lengths in the ratio a:b. If the radius of the circle is r, then the area of the triangle is:
A triangle is drawn with its vertices on the circle C such that one of its sides is a diameter of C and the other two sides have their lengths in the ratio a:b. If the radius of the circle is r, then the area of the triangle is:
Options
Answer: 2abr²/(a²+b²)
Explanation:
Since one side is diameter, the triangle is right-angled (Thales theorem). Let the two sides be ak and bk. By Pythagoras: (ak)² + (bk)² = (2r)². Solve for k, then area = (1/2) × ak × bk = 2abr²/(a²+b²).
Explanation:
Since one side is diameter, the triangle is right-angled (Thales theorem). Let the two sides be ak and bk. By Pythagoras: (ak)² + (bk)² = (2r)². Solve for k, then area = (1/2) × ak × bk = 2abr²/(a²+b²).
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