The diameter will always pass through the center of the circle. In the circle below, ∠ Y is a right angle if and only if XZis a diameter of the circle.Ī quadrilateral can be inscribed in a circle if and only if its opposite angles are supplementary. The diameter is the distance from one side of the circle to the other at its widest points. Conversely, if one side of an inscribed triangle is a diameter of the circle, then the triangle is a right triangle and the angle opposite the diameter is the right angle. If a right triangle is inscribed in a circle, then the hypotenuse is a diameter of the circle. In the circle below, the measure of ∠ QRS is 1/ 2 of the measure of arc QS. The formula for the area of a circle is better known in terms of the radius: The radius can be found from the diameter. If an angle is inscribed in a circle, then its measure is half the measure of its intercepted arc. If one chord is a perpendicular bisector of another chord, then the first chord is a diameter. If the diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc. Therefore the point P shown below is called the midpoint, and arc PQ ≅ arc PR if and only if PQ ≅ PR. Diameter can be found by multiplying the. In the same circle, two minor arcs are congruent if and only if their corresponding chords are congruent. The length of a straight line that intersects the center point of the circle and reaches to each side of the boundary.
In the example below, the measure of arc BC is 35 o. The measure of an arc is defined by the measure of its central angle.
If the measure of ∠ADB is less than 180°, then the interior of ∠ ADB forms the minor arc while the exterior forms the major arc. In the circle below, ∠ ADB is a central angle. What is the radius of the garden?Īn angle whose vertex is on the center of a circle is called a central angle. The distance from Jason to a point of tangency on the garden is 56 feet. Jason is located at a point P, 28 feet from the edge of a circular garden. If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency. In the circle below, line F is a tangent. A tangent is a line that intersects with the circle at only one point. A diameter is a chord that passes through the center of the circle.Ī secant is a line that intersects with a circle at two different points. In the circle above, ACis a diameter of the circle.Ī chord is a segment that also has endpoints on the circle, but does not need to cross through the center. For the circle below, AD, DB, and DCare radii of a circle with center D.Ī line segment that crosses the circle by passing through its center is called a diameter. The diameter is twice the length of the radius. A radius is a line segment with one endpoint at the center of the circle and the other endpoint on the circle. The distance from a circle's center to a point on the circle is called the radius of the circle. A circle is a set of all points in a plane that are all an equal distance from a single point, the center.
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