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Maths Formulas For Class 9: Important Class 9 Mathematics Formulas Two figures are congruent, if they are of the same shape and of the same size. Two circles of the same radii are congruent. Two squares of the same sides are congruent. If two triangles ABC and PQR are congruent under the correspondence A � P, B-Q and C-R, then symbolically, it . Class 9 Maths notes according to FBISE syllabus. Contains solved exercises, review questions, MCQs, important questions and chapter overview.
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We will work on your suggestions as soon as possible. Your support is what keeps us going. Class IX Mathematics Notes. Contains solved exercises, review questions, MCQs, important board questions and chapter overview.

Unit 2 - Real and Complex Numbers Exercise 2. Unit 3 - Logarithms Exercise 3. Unit 5 - Factorization Exercise 5. Unit 10 - Congruent Triangles Theorem Unit 11 - Parallelograms and Triangles Theorem Unit 13 - Sides and Angles of Triangles Theorem Unit 15 - Pythagoras' Theorem Theorem Unit 17 - Practical Geometry Triangles Exercise Glossary Glossary.

Join OE. If two equal chords of a circle intersect within the circle, prove that the line joining the point of intersection to the centre makes equal angles with the chords.

Solution: Given : Two circles with the common centre O. Three girls Reshma, Salma and Mandip Ch 6 Maths Class 10 Theorems Kit are playing a game by standing on a circle of radius 5m drawn in a park. If the distance between Reshma and Salma and between Salma and Mandip is 6 m each, what is the distance between Reshma and Mandip?

A circular park of radius 20 m is situated in a colony. Three boys Ankur, Syed and David are sitting at equal distance on its boundary each having a toy telephone in his hands to talk each other.

Find the length of the string of each phone. Let the length of each side of the equilateral triangle be 2x. A chord of a circle is equal to the radius of the circle, find the angle subtended by the chord at a point on the minor arc and also at a point on the major arc. Solution: We have a circle having a chord AB equal to radius of the circle. Solution: The angle subtended by an arc of a circle at its centre is twice the angle subtended by the same arc at a point pn the circumference.

In figure, A, B and C are four points on a 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 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, find the radius Ch 6 Maths Class 10 Theorems Mac 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 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 Ch 10 Maths Class 10 Theorems Editor 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.

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