Question

basic concept and theorem in circle

Answer 1

inner circle there is only a single tangent passes through a point of contact and from external point P there can be only two tangents touches with the circle and tangents are perpendicular to the radii

Answer 2

Definition:A circle is a simple closed figure in which all the points that lie on

Radius: The line segment that connects the center of the circle to any point on the circle is called radius. OB, OA, OX, OY are the different radii of the circle in the figure above. Infinite number of radii can be drawn for any circle.

Diameter: The line segment that passes through the center and connects two points on the circle is called the diameter. AB is the diameter of the circle. Like radius, infinite number of diameters can bedrawn in a circle.
Diameter = 2 * radius
Or
Radius = Diameter / 2

Chord: The line segment that connects anytwo points on a circle is a chord. Infinite number of chords can be drawn in a circle. XY is a chord of the circle.Apparently, the diameter is the longest chord of a circle.

Circumference:The measure of the distance around the edge of a circle is the circumference of thecircle.The circumference of a circle is given by the formula,C = 2prWhere C is the circumference and r is the radius.Since 2*radius = diameter, Circumference is also given byC = pdThe value of p is approximately 22/7 or 3.14159.

Area:The area of a circle is given by the formula,A = pr2Where r is the radius of the circle.Since r=d/2, Area is also given byA = pd2/4

Arcs and sectors:An arc is a part of the circumference of thecircle. XY is an arc in the figure above.A sector is the area covered by two radii and the arc connecting them. XLY and XOYare two of the sectors in the figure above.Length of an arc is given by the formula, (x/360) * 2prArea of a sector is given by the formula, (x/360) * pr2Where x is the angle subtended by the arc and r is the radius

Inscribed angle:The angle whose one vertex lies on one part of the circle and the other two end points lie on other place on the circle, is called an inscribed angle. ∠XLY, ∠OXY, ∠OYX are some of the inscribed angles in the figure above.Inscribed angles subtended by the same arc are equal.A central angle is twice the corresponding inscribed angle.In the figure above,∠XOY = 2 ∠XLY

Tangent:A tangent of a circle is a line that just touches the circle at one point without intersecting it.

Circumscribed circle: If a polygon is present inside a circle in such a way that all its vertices lie on the circle, or just touchthe circle, then the circle is called a circumscribed circle.