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It is the consequence of one of the circle theorems and in some books, it is considered a theorem itself. The underlying proposition is that the angle subtended at the circumference of the circle by any arc of a circle is half the angle subtended at the centre.

In the case of a semicircle, the arc is the half circle and the angle at the centre is the one that the diameter makes at the centre of the circle ie 180 degrees. So the angle at the circumference is half that ie 90 degrees.

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Q: Why is an inscribed angle that intercepts a semi-circle a right angle?

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a right angle

Right Angle?

A right angle triangle will fit into a semicircle.

A semi circle is made up of two right angles.

A right angle triangle can fit into a semi-circle

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A right angle.

a right angle

It is a right angle.

Right Angle?

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.

35 I believe.

All triangles inscribed in a semicircle with one side of the triangle being the diameter of the semicircle are right triangles.

Yes. It follows from one of the circle theorems which states that the angle subtended in a semicircle is a right angle.

A right angle triangle will fit into a semicircle.

A semi circle is made up of two right angles.

A right angle triangle can fit into a semi-circle

A straight angle is 180 degrees, or twice the measure of a right angle. Therefore, it looks like a right angle that has been folded out into a flat line. Another way is to look at the arch of a 180 degree angle as a semicircle. Connect both ends of the semicircle and you have a straight line.

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