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To find the angle of a triangle within a circle segment, you first need to determine the central angle of the circle segment. Then, you can use the properties of triangles inscribed in circles to find the angle. The angle of the triangle within the circle segment will be half the measure of the central angle.
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How would you construct an isosceles triangle if only given the vertex angle and the radius of the circumscribed circle?
You have an isosceles triangle, and a circle that is drawn around it. You know the vertex angle of the isosceles triangle, and you know the radius of the circle. If you use a compass and draw the circle according to its radius, you can begin your construction. First, draw a bisecting cord vertically down the middle. This bisects the circle, and it will also bisect your isosceles triangle. At the top of this cord will be the vertex of your isosceles triangle. Now is the time to work with the angle of the vertex. Take the given angle and divide it in two. Then take that resulting angle and, using your protractor, mark the angle from the point at the top of the cord you drew. Then draw in a line segment from the "vertex point" and extend it until it intersects the circle. This new cord represents one side of the isosceles triangle you wished to construct. Repeat the process on the other side of the vertical line you bisected the circle with. Lastly, draw in a line segment between the points where the two sides of your triangle intersect the circle, and that will be the base of your isosceles triangle.
What relationship does the hypotenuse have with the circle?
The hypotenuse has no intrinsic relationship to the circle. The hypotenuse is the side of a right triangle that is opposite to the right angle. You can draw a circle that has a hypotenuse as its diameter or its radius, but you can do that with any line segment. It would not be related in another way to the triangle.
What is A segment that connects a vertex of a triangle to the opposite side of the triangle at a right angle?
The hypotenuse of a right angle triangle is opposite to its right angle of 90 degrees.
What is angle of inscribed in semi circle?
A right angle triangle can fit into a semi-circle
What is a triangle in a circle that is formed by two chords and a diameter?
If a triangle is drawn in a circle with a diameter as the base of the triangle, then the angle opposite that diameter is a right angle. This is an extension of the theorem that the angle which an arc of a circle subtends at the centre of a circle is twice the angle which the arc subtends at the circumference. In the case of a diameter, then the angle subtended at the centre is 180° and thus the angle at the circumference is 90°.
