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Equal chords are subtended by equal angles from the center of the circle. A chord that passes through the center of a circle is called a diameter and is the longest chord of that specific circle. If the line extensions (secant lines) of chords AB and CD intersect at a point P, then their lengths satisfy AP·PB = CP·PD (power of a point theorem).
- Circle
- Diameter
- Chord
- Radius
- Arc
- Tangent
- Parts of A Circle
In geometry, a circle is a closed curve formed by a set of pointson a plane that are the same distance from its center O. Thatdistance is known as the radiusof the circle.
The diameter of a circle is a line segmentthat passesthrough the center of the circle and has its endpoints on the circle. All the diameters of thesame circle have the same length.
A chordis a line segment with both endpoints on the circle. The diameter is a specialchord that passes through the center of the circle. The diameter would be the longest chordin the circle.
The radius of the circle is a line segmentfrom the centerof the circle to a point on the circle. The plural of radius is radii. In the above diagram, O is the center of the circle and and are radii of the circle. The radii of a circle are all the same length. The radius is half thelength of the diameter.
An arc is a part of a circle. In the diagram above, the part of the circle from B to C forms an arc. An arc can be measured in degrees. In the circle above, arc BC is equal to the ∠BOCthat is 45°.
A tangent is a line that touches a circle at only one point.A tangent is perpendicularto the radius at the point ofcontact. The point of tangency is where a tangent line touches the circle. In the above diagram, the line containing the points B and C is a tangent to the circle. It touches the circle at point B and is perpendicular to the radius.Poi...
The following video gives the definitions of a circle, a radius, a chord, a diameter, secant, secant line, tangent, congruent circles, concentric circles, and intersecting circles. A secant lineintersects the circle in two points. A tangentis a line that intersects the circle at one point. A point of tangencyis where a tangent line touches or inter...
The Converse of this Theorem: The line drawn through the centre of a circle to bisect a chord is perpendicular to the chord. Proof: Consider the same figure, as given above. Assume that AB is the chord of a circle with centre “O”. The centre “O” is joined to the midpoint “X” of the chord AB. Now, we need to prove OX ⊥ AB.
Diameter is the line segment that passes through the center of a circle touching two points on the circumference of the circle. A chord is a line segment that joins any two points on the circumference of the circle. How to Draw the Chord of a Circle? The chord of a circle can be constructed with the help of a compass and a ruler. For example ...
A line that: is perpendicular to the chord; bisects (cuts in half) the chord; passes through the center of the circle. If a line through a chord has two of these properties, it also has the third. A line that is perpendicular to a chord and bisects it must pass through the center of the circle.
Answer. Since 𝑀 is the center of the circle and line 𝑀 𝐷 bisects chord 𝐴 𝐵 at 𝐶, we can apply the chord bisector theorem, which states that if we have a circle with center 𝑀 containing a chord 𝐴 𝐵, then the straight line that passes through 𝑀 and bisects chord 𝐴 𝐵 is perpendicular to 𝐴 𝐵. Hence, we can ...
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The perpendicular bisector of a chord is a line passing through the center of the circle such that it divides the chord into two equal parts and meets the chord at a right angle. A circle is a 2D figure without corners or edges such that all the points on the boundary are equidistant from the center. The line segment connecting the center with ...
