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What is the relation between the arc length and angle for a sector of a circle?
A sector is the area enclosed by two radii of a circle and their intercepted arc, and the angle that is formed by these radii, is called a central angle. A central angle is measured by its intercepted arc. It has the same number of degrees as the arc it intercepts. For example, a central angle which is a right angle intercepts a 90 degrees arc; a 30 degrees central angle intercepts a 30 degrees arc, and a central angle which is a straight angle intercepts a semicircle of 180 degrees. Whereas, an inscribed angle is an angle whose vertex is on the circle and whose sides are chords. An inscribed angle is also measured by its intercepted arc. But, it has one half of the number of degrees of the arc it intercepts. For example, an inscribed angle which is a right angle intercepts a 180 degrees arc. So, we can say that an angle inscribed in a semicircle is a right angle; a 30 degrees inscribed angle intercepts a 60 degrees arc. In the same or congruent circles, congruent inscribed angles have congruent intercepted arcs.
The central angle of a semicircle is what kind of angle?
It's a STRAIGHT angle
How do you find the measure of the central angle?
the measure of the inscribed angle is______ its corresponding central angle
Is an inscribed angle which intercepts a major arc an obtuse angle?
Well, not always. An obtuse angle is one that is greater than 90 degrees. Any inscribed angle that intercepts a major arc can be any measurement in which it intercepts.
Prove that the sum of perimeter of inscribed semicircle is equal to the perimeter of outside semicircle?
The circumference of the large semicircle is pi-r radius of the smaller semi circles are r1 r2 r3 r4... thus their circumference is pi-r1 pi-r2 so on.. pi-r = pi(r1+r2+r3..)
What is the angle inscribed in a semicircle?
It is a right angle.
What kind of angle is inscribed in a semicircle?
Right Angle?
What angle inscribed in semicircle?
180 degrees
What kind of an angle is the inscribed angle that intercepts a semicircle.?
A right angle.
Is every inscribed angle that intercepts a semicircle is a right angle or an acute angle or a obtuse angle?
a right angle
Any inscribed in a semicircle is a?
All triangles inscribed in a semicircle with one side of the triangle being the diameter of the semicircle are right triangles.
What is the relation between the arc length and angle for a sector of a circle?
A sector is the area enclosed by two radii of a circle and their intercepted arc, and the angle that is formed by these radii, is called a central angle. A central angle is measured by its intercepted arc. It has the same number of degrees as the arc it intercepts. For example, a central angle which is a right angle intercepts a 90 degrees arc; a 30 degrees central angle intercepts a 30 degrees arc, and a central angle which is a straight angle intercepts a semicircle of 180 degrees. Whereas, an inscribed angle is an angle whose vertex is on the circle and whose sides are chords. An inscribed angle is also measured by its intercepted arc. But, it has one half of the number of degrees of the arc it intercepts. For example, an inscribed angle which is a right angle intercepts a 180 degrees arc. So, we can say that an angle inscribed in a semicircle is a right angle; a 30 degrees inscribed angle intercepts a 60 degrees arc. In the same or congruent circles, congruent inscribed angles have congruent intercepted arcs.
When a triangle with one side length the diameter of a circle is inscribed in that circle does it have to be a right triangle?
Yes. It follows from one of the circle theorems which states that the angle subtended in a semicircle is a right angle.
What is a triangle in a semicircle?
A right angle triangle will fit into a semicircle.
What is a inscribed angle?
An inscribed angle is an angle with its vertex on a circle and with sides that contain chords of the circle.
The central angle of a semicircle is what kind of angle?
It's a STRAIGHT angle
What is the center of an inscribed angle called?
The center of an inscribed angle is either a vertex or an endpoint.
