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Oct 4, 2024 · Angle formed by the two lines drawn from the endpoints of the diameter at any point on the semicircle is called as the angle inscribed in a semicircle. Angle inscribed in a semicircle is equal to 90° i.e., right angle. The diameter of semicircle has an angle of 180°as it is a straight line. People Also Read: Geometric Shapes; Volume Formulas
PR is the diameter of a circle centered on O; its radius AO is the arithmetic mean of a and b. Using the geometric mean theorem, triangle PGR's altitude GQ is the geometric mean. For any ratio a:b, AO ≥ GQ. A semicircle can be used to construct the arithmetic and geometric means of two lengths using straight-edge and compass.
The inscribed angle is the angle formed by the line segments drawn from each end of the diameter to any point on the semicircle. No matter where the line touches the semicircle, the angle that is inscribed is always 90°. In the below image, we can see that angle B is at 90 degrees, and the diameter AC is 180°. Since a semicircle is half of a ...
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- Angle Inscribed in A Semicircle
‘Semi’ means half, thus semicircle is a half-circle. It is formed when a line passing through the center of the circle touches the two ends forming an intercepted arc. Thus a semicircle consists of the diameter of the circle and its connecting arc. Semicircle being half a circle, its arc always measures (360°/2 = 180°) and thus is referred to as a ...
Area
The area of a semicircle is the space enclosed by the semicircle. Since a semicircle is exactly half a circle, its formula can be obtained by dividing the area of a circle by 2. As we know, Area of a Circle = πr2 Thus, Area of a semicircle = πr2/2, here π = 3.141, r= radius The area of a semicircle is expressed in square units (m2, cm2,etc) Let us solve an example to clear your concept.
Perimeter
The perimeter of a semicircle is the sum of half the circle’s circumference, plus the diameter of the semicircle. It is also called the circumference of a semicircle. Thus, it is not half the perimeter of a circle. As the perimeter of a circle is given by 2πr or πd So, the perimeter of the semicircle = ½ (2πr) + d =>πr + d =>πr + 2r, here π = 3.141, r= radius or, ½ πd + d, here π = 3.141, d= diameter The perimeter of a semicircle is expressed in units of m, cm, etc. Let us solve an example to...
An inscribed angle of a semicircle is an angle formed by drawing a line from each endpoint of the diameter to a point on the semicircle arc. Thus, an inscribed angle has a measure that is half the measure of the arc that subtends it. Since a semicircle is half of a circle the angle subtended by the arc that forms the semicircle measures 180°. There...
The angle written is always 90°, no matter where another line intersects the semicircle. The angle B in the figure below is 90 degrees, while the diameter length AC is 180 degrees. Because the semicircle equals half of the circle, the angle generated by an arc that transforms the circle into a semicircle is 180°. Inscribed Angle in a Semicircle
An angle inscribed in a semicircle is always a right angle. This geometric property is frequently leveraged in Euclidean geometry. Proof: Imagine a circle centered at O with a diameter AB. Select any point C on the semicircle that is bounded by A and B. The goal is to prove that angle ACB forms a right angle (90°). Draw the line OC.
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Semi Circle Shape. When a circle is cut into two halves or when the circumference of a circle is divided by 2, we get a semicircular shape. Since a semicircle is half that of a circle, hence the area will be half that of a circle. In the below figure, the line AC is called the diameter of the circle.
