0
What is the angle subtended by the circumference of a circle at its centre?
Wiki User
∙ 10y ago
It is 360 degrees because angles around a point add up to 360 degrees
Wiki User
∙ 10y ago
Add your answer:
Earn +20 pts
Why is an inscribed angle that intercepts a semi-circle a right angle?
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.
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°.
How do you draw an angle 110 degree using ruler and compass?
Construct a circle and divide the circumference into 36 equal arcs Each arc will represent 10 degrees and 11 of them subtended to the circle's centre will create an obtuse angle of 110 degrees
When a body moves along a semicircle total angle subtended by it at centre of circle is?
Pie/2=22/7/2Angle in radians =Total length of the arc/radius of the circle
How do you define radian?
An informal definition: If you take a radius of a circle and wrap it around its circumference then the angle which that arc will make at the centre of the circle is 1 radian.More formally, a radian is 1/(2*pi) of a whole angle.
Why is an inscribed angle that intercepts a semi-circle a right angle?
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.
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°.
What is an angle whose vertex whose vetex is the center of a circle?
It will be the same angle subtended by its circumference.
How do you find radius when arc length is given?
Let us recall the formula for the circumference of a circle. That one is 2pi r. r is the radius of the circle and 2pi is the angle in radian measure subtended by the entire circle at the centre. If this is so, then any arc length 'l' will be equal to the product of the angle in radian measure subtended by the arc at the centre and the radius.So l = theta r. Say theta is the angle subtended by the arc at the centre.Therefrom, r = l / Theta.
What is a 90 degree angle subtended by?
May things, but the probable answer sought here is a diameter of a circle, at the circumference of the circle.
How do you draw an angle 110 degree using ruler and compass?
Construct a circle and divide the circumference into 36 equal arcs Each arc will represent 10 degrees and 11 of them subtended to the circle's centre will create an obtuse angle of 110 degrees
Why is it that a quadrilateral can be inscribed in a circle if and only if its opposite angles are supplementary?
Because of one of the Circle Theorems that states that the angle subtended by any arc at the centre of the circle is half that at the circumference. A rough version of the proof follows: Suppose the quadrilateral ABCD is inscribed in a circle with centre O. Join AO and CO. This partitions the circumference into two arcs - both AC but going around different sides of the centre. One of the arcs AC, subtends angle B at the circumference and suppose the angle subtended by the same arc at O is X. Then 2B = X The other arc AC subtends angle D at the circumference and suppose the angle subtended by the same arc at O is Y. Then 2D = Y So 2B + 2D = X + Y But X + Y = 360 degrees. So B + D = 180 that is, B and D are supplementary. And then, since A+B+C+D = 360, A + C = 180. The converse can be proved similarly.
What is the name for 90 degrees in the circle?
If an arc of a circle is drawn so that the length of the arc is equal to the radius of the circle then the angle at the centre of the circle subtended by the arc is called one radian.Then the angle subtended by the entire circle is given by the ratio , circumference / radius = 2πr/r = 2π radians.2π radians is equivalent to 360°So, π radians = 180°and thus, π/2 radians = 90°Pi over two, or Pi divided by two radians is the name for 90° in a circle.
How to find length of arc if radius and angle subtended at the center are given?
Full circumference of the circle = (2 pi) times (radius)Arc is a fraction of the full circumference.The fraction is (angle subtended at the center) divided by (360 degrees).If you have the radius 'R' and the angle 'A', the length of the arc is(pi) (R) (A) / 180
The sum of the measures of the angles is 180 degrees?
The question probably refers to the internal angles of a triangle which total 180° . Also, the angle at the centre of a circle and subtended by half the circle is 180°.
What do you call the angle whose vertex is at the center of the circle and whose sides are the radii of the circle?
It is the subtended angle of the arc
What is the angle subtended by an arc of a circle equal in length to the radius of that circle?
The answer does not match. It is called a Radianthat is used in Trigonometry, a special branch of mathematics which deals with study of triangles. "Tri" means three and "gono" means angle and "metry" means measure) . If there is an angle at the center of circle subtended by the arc whose length is equal to the radius, then the angle at the center is called 1 Radian.Extending the math out in order to determine the number of degrees in one radian, this is what we have. C = 2(pi)r; the length of the circumference is 2(pi) times the radius. This means that the number of radii in the circumference is 2(pi); there are 2(pi) radii in the circumference. There are 360 degrees in a circle, so the number of degrees in an angle subtended by an arc one radius long would be 360/2(pi), or about 57.3 degrees.
