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Prove that, if chords of congruent circles subtend equal angles at their centres, then the chords are equal. Draw different pairs of circles. How many points does each pair have in common?
What is the maximum number of common points? Solution: Let us draw different pairs of circles as shown below: We have. Suppose you are given a circle. Give a construction to find its centre.
Solution: Steps of construction : Step I : Take any three points on the given circle. Let these points be A, B and C. If two circles intersect at two points, prove that their centres lie on the perpendicular bisector of the common chord. Two circles of radii 5 cm and 3 cm intersect at two points and the distance between their centres is 4 cm. Find the length of the common chord. Let PQ be the common chord. If two equal chords of a circle intersect within the circle, prove that the segments of one chord are equal to corresponding segments of the other chord.
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 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 Class 9 Maths Ch 10 Ex 10.2 English 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.
The radius of the circle is a 7 cm b 12 cm c 15 cm d Prove that the tangents drawn at the ends of a diameter of a circle are parallel. Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre. The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle.
Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle. A quadrilateral ABCD is drawn to circumscribe a circle see figure. Prove that the angle between the two tangents drawn from an external point Class 8 Maths Ch 10 Ex 10.2 Iso to a circle is supplementary to the angle subtended by the line segment joining the points of contact at the centre.
Prove that the parallelogram circumscribing a circle is a rhombus.
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