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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..)
