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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 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. A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively see figure. Find the sides AB and AC. Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle. Solution: Ex 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: Ch 10 Maths Class 10 Ex 10.2 Inc 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 Class 9 Maths Ch 10 Ex 10.2 Inch 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 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 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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