The line drawn through the center of a circle to bisect a chord is perpendicular to the chord. Given: A circle with center O, AB is chord of a circle and OC bisect chord at C. i,e. AC = CB. To prove: OC ⊥ AB Construction: join OA and OB. Proof: In △ OCA and △ OCB OA = OB (Radius […]
Read More →The perpendicular from the center of a circle to a chord bisects the chord. Given: A circle with center O, AB is chord of a circle and OC perpendicular from the center O to the chord AB. i.e. OC ⊥ AB therefore ∠OCA and ∠OCB, Both angles are 900. To prove: AC = CB Construction: join OA and OB. Proof: In △OCA and △ OCB ∠OCA = ∠OCB […]
Read More →Radius of a Circle The radius name comes from the Latin and its meaning is ray. Definition: Radius The distance from center of a circle to any point on the circle, or a line from center to any point on the circumference of a circle is known as “Radius”, of a circle. The […]
Read More →Definition, Properties, Examples – Cyclic Quadrilaterals What is a Cyclic Quadrilateral A cyclic quadrilateral is a four sided polygon that is inscribed in a circle. The vertices are said concyclic. The center of the circle is called circumcenter and radius of the circle is called circumradius. Definition: A Cyclic Quadrilateral is a quadrilateral, whose all four vertices […]
Read More →If the angles subtended by chords of a circle at the center are equal, then the chords are equal. Given: A circle with center O, AB and CD are chords of circle that subtend equal angles at center O. i,e. ∠AOB = ∠COD. To prove: chord AB = chord CD Proof: In △AOB and △ CODOA = OC (Radius of circle)∠AOB […]
Read More →Equal chords of a circle subtend equal angles at the center. Given: Two equal chords AB and CD of a circle with center O. i,e. AB = CD. To prove: ∠AOB = ∠COD Proof: In △AOB and △ COD OA = OC (Radius of circle)OB = OD (Radius of circle)AB = CD (Given) Hence, △AOB ≅ △ COD (SSS Congruence rule) ∴ ∠AOB […]
Read More →Tangent of a Circle Definition & Example In this lesson we will learn about tangent of a circle, before understanding the concept of a circle, let us know about circle. Circle Definition: A circle is a collection of all the points in a plane, whose all points are same distance from a fix point, is called “Circle”. […]
Read More →Circumscribes and Inscribed Circles Circumscribed Circle The circumscribed circle is one and only one circle that always passes through all three vertices (corners) of the triangle. The center of the circumscribed circle is a point where all the three perpendicular bisectors of the triangles sides are meet. The center of the circumscribed circle is known ascircumcenter of the triangle. […]
Read More →Circumscribed and Inscribed Circle 1. Circumscribed circle In geometry, the Circumscribed circle or circumcircle of a polygon is a circle that passes inside a circle in such a way that all its vertices lie on the circle, or just touch the circle. Centre of this circle is called circumcenter and its radius is called […]
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