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ABCD is a cyclic quadrilateral in which AB = BC, O is the centre of circle and one of diagonal of cyclic quadrilateral passes through the centre of circle and ∠DCA = 40°. Find the ∠BAD.
ABCD is a cyclic quadrilateral in which AB = BC = 8 cm, O is the center of the circle and one of the diagonal of the cyclic quadrilateral passes through the center of the circle. Find the radius of the circle.
ABCD is a cyclic quadrilateral in which O is the center of the circle and one of the diagonal of the cyclic quadrilateral passes through the center of the circle and ∠DCA = 30°. Find the measure of ∠CAD.
ABCD is a cyclic quadrilateral in which AB = BC = 6 cm, O is the center of the circle and one of the diagonals of the cyclic quadrilateral passes through the center of the circle. Find the area of ΔABC.
Which of the following propertie(s) of circle is/are correct? I. Opposite angles of a cyclic quadrilateral are supplementary. ABCD is cyclic quadrilateral as its vertices lie on the circle. II. The degree measure of an arc is equal to twice the measure of an angle inscribed in the opposite arc.
Which of the following statements is/are true? A: If two tangents, PA and PB, are formed on a circle from a point ‘P’ and OA and OB are the radius of the circle, then OAPB will be a cyclic quadrilateral. B: In a ΔABC, an incircle is formed with centre ‘O’. Then ∠BAC will be 180° less than the double of the angle made by side BC at the centre of the circle. C: The length of two tangents from a point, outside the circle, are always equal.
Consider the following a) Opposite angles of a cyclic quadrilateral are complementary b) The angle at the centre of a circle is twice the angle at the circumference. c) A cyclic quadrilateral has all its vertices on the circumference of the circle Which of the above statement is/are correct?
Which of the following statements is/are true? A: If a circle is formed from a wire, which was initially in the shape of a semi-circle, then ratio of radius of circle and that of semi-circle will be 7: 11. B: If in a semi-circle of radius ‘r’, another semi-circle of radius ‘4r/5’ is drawn, then area of the remaining part of larger semi-circle will be ‘3πr2/5’. C: In a circle of radius ‘r’, if ‘O’ is the center of circle and radii OA and OB are at the angle of 45°, then the length of major arc AB will be ‘7πr/8’.
Given steps in procedure to find the center of gravity of the quadrilateral ABCD. Arrange the steps. i. Draw lines joining G1 with G2 and G3 with G4. ii. In given quadrilateral draw diagonal BD and locate centers of gravity G1, G2 of triangles BCD and ABD. iii. The point of intersection of lines G1G2 and G3G4 gives the center of gravity of the quadrilateral ABCD. iv. Similarly draw the diagonal AC and determine the centers of gravity G3, G4 of triangles ABC and ADC.
A quadrilateral ABCD is inscribed in a circle. The sides AB and DC are extended to meet at point M outside the circle with BM = 9 cm, MC = 12 cm and MD = 30 cm. What is the value of side AB of quadrilateral ABCD?