Note: i Diameter is the longest chord in a circle. Note: i A diameter of a circle divides it into two equal arcs, each of which is Ch Theorems 9 Maths Solution 10 Class called a semicircle. The region consisting of ch 10 maths class 9 theorems solution points lying on the circumference of a circle and inside it Ch 10 Maths Class 9 Theorems Solution is called the interior of the circle. 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 Ch 10 Maths Class 9 Theorems Solution 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 Ch 10 Maths Class 9 Theorems Solution ch 10 maths class 9 theorems solution through three given non-collinear points. Statement: Equal chords of a circle or of congruent circles are equidistant from the centre or ch 10 maths class 9 theorems solution. Given: AB and CD are two equal chords of a circle.
Statement: The Ch 10 Maths Class 9 Theorems Solution angle subtended by an arc at the centre is double the angle Ch 10 Maths Class 9 Theorems Solution subtended by it at any point on the remaining part of the circle. In Ch Theorems 10 Class Maths Solution 9 fig. Statement: If a line segment joining two points subtends equal angles at two other points lying on the same side of the line containing the line segment, the four points lie on a circle i.
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Find the length of the string of each phone. Let the length of each side of the Ch 10 Maths Class 9 Theorems Solution 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 Class Maths Solution 10 Ch 9 Theorems 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 Ch 10 Maths Class 9 Theorems Solution 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 Ch 10 Maths Class 9 Theorems Solution that a cyclic parallelogram is a rectangle.
Since, ABCD is a Ch 10 Maths Class 9 Theorems Solution 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 Ch 10 Maths Class 9 Theorems Solution 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 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 Ch 10 Maths Class 9 Theorems Solution 4 cm from the centre, what is the distance of the other chord from the centre? Parallel chords AB Ncert Solutions For Class 10 Maths Ch 12 Ex 12.2 Map 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: 10 Maths Class Ch 9 Solution ThCh 10 Maths Class 9 Theorems Solution eorems An exterior angle of a triangle is equal to the sum of interior opposite angles. Prove that the circle drawn with any side Ch 10 Maths Class 9 Theorems Solution Ch 10 Maths Class 9 Theorems Solution of a rhombus as diameter, passes through the point of intersection of its diagonals.
Taking AB as diameter, a circle is drawn. A circle 10 Theorems 9 Class Ch Solution Maths 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 Ch 10 Maths Class 9 Theorems Solution chords of a circle which bisect each other. Similarly, AC is a Class Solution 10 Maths Theorems 9 Ch Ch 10 Maths Class 9 Theorems Solution Ch 10 Maths Class 9 Theorems Solution diameter. All the questions are explained well using the theorems of circles 9 Ch Class Solution 10 Maths Theorems and giving proper examples.
In few questions some axioms of circles are also 9 Maths Theorems Solution Class 10 Ch used as theorems. Study Material for What do understand by a circle? What are the components of a circle? What are the main Properties related to a circle?
Important Theorems on Circles Class 9 Maths Chapter 10 Equal chords of a circle are equidistant from the centre and cords equidistant from the centre of a circle are equal. If two arcs Ch 10 Maths Class 9 Theorems Solution Ch 10 Maths Class 9 Theorems Solution of a circle are congruent, then their corresponding chords are equal and conversely if two chords of a circle are equal, then their corresponding arcs are congruent. Congruent arcs of a circle subtend equal angles at the centre.
The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part Ch 10 Maths Class 9 Theorems Solution of the circle. Angles in the same segment of a circle are equal. Angle in a semi-circle is a right angle. The sum of Ch 10 Maths Class 9 Theorems Solution either pair of opposite angles of a cyclic quadrilateral is and if the sum of a pair of opposite angles of a quadrilateral is , then the quadrilateral is cyclic.
The centre of a circle lies in interior Class 9 Solution Ch 10 Maths Theorems of the circle. A circle has only finite number of equal chords. True or False? Because, there are infinite number of equal chords in Ch 10 Maths Class 9 Theorems Solution a circle. Sector is the region between the chord and its corresponding arc.
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