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NCERT Solutions for Class 9 Maths Chapter 10 Circles in PDF Maths model is an intellectual model that uses mathematical expression to explain the function of a system. In schools, students are assigned Maths projects to make them think and learn. They can use their intellectual abilities to create models. These models will help to learn the concepts in a creative way.
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The region consisting of all points lying outside a circle is called the exterior of the circle. The region consisting of all points which are either on the circle or lie inside the circle is called the circular region. Fundamentals of Circles. Statement: If the angles subtended by the chords of a circle at the centre are equal, then the chords are equal. Statement: The line drawn through the centre of a circle to bisect a chord is perpendicular to the chord.

Statement: There is one and only one circle passing through three given non-collinear points. Statement: Equal chords of a circle or of congruent circles are equidistant from the centre or centres. Given: AB and CD are two equal chords of a circle. Statement: The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.

ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. Solution: Since angles in the same segment of a circle are equal. If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that it is a rectangle. If the non � parallel sides of a trapezium are equal, prove that it is cyclic.

Two circles intersect at two points B and C. Solution: Since, angles in the same segment of a circle are equal. If circles are drawn taking two sides of a triangle as diameters, prove that the point of intersection of these circles lie on the third side. They intersect at a point D, other than A. Let us join A and D. Thus, D lies on BC. Case � I: If both the triangles are in the same semi-circle. Join BD. DC is a chord. Case � II : If both the triangles are not in the same semi-circle.

Prove that a cyclic parallelogram is a rectangle. Since, ABCD is Ch 6 Maths Class 10 Theorems Android a cyclic quadrilateral. Thus, ABCD is a rectangle. Prove that the line of centres of two intersecting circles subtends equal angles at the two points of intersection. Two chords AB and CD of lengths 5 cm and 11 cm, respectively of a circle are parallel to each other and are on opposite sides of its centre. If the distance between AB and CD is 6 cm, Ch 2 Maths Class 10 Byjus Model find the radius of the circle. Solution: We have a circle with centre O.

Let r cm be the radius of the circle. The lengths of two parallel chords of a Ch 10 Maths Class 10 Theorems And circle are 6 cm and 8 cm. If the smaller chord is at distance 4 cm from the centre, what is the distance of the other chord from the centre? Parallel chords AB and CD are such that the smaller chord is 4 cm away from the centre.

Let the vertex of an angle ABC be located outside a circle and let the sides of the angle intersect equal chords AD and CE with the circle. Proof: An exterior angle of a triangle is equal to the sum of interior opposite angles. Prove that the circle drawn with any side of a rhombus as diameter, passes through the point of intersection of its diagonals. Taking AB as diameter, a circle is drawn. A circle drawn with Q as centre, will pass through A, B and O.

ABCD is a parallelogram. ABCE is a cyclic quadrilateral. AC and BD are chords of a circle which bisect each other. Similarly, AC is a diameter. Since, opposite angles of a parallelogram are equal. Two congruent circles intersect each other at points A and B. Solution: We have two congruent circles such that they intersect each other at A and B.

A line segment passing through A, meets the circles at P and Q. Let us draw the common chord AB. Since angles subtended by equal chords in the congruent circles are equal.

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