CBSE Guess > Papers > Important Questions > Class X > Maths > Mathematics By Mr. Sanjay Kumar

Chapter - 9

Q. 96. Prove that the line joining the mid-points of two parallel chords of a circle passes through the centre of the circle.

Q. 97. Prove that the line joining the mid-points of two equal chords of a circle makes equal angles with these chords.

Q. 98. If two non-parallel sides of a trapezium are equal, then prove that it is cyclic.

Q. 99. Prove that the quadrilateral formed by angle bisectors of a cyclic quadrilateral is also cyclic.

Q. 100. Two circles of radii 10 cm and 8 cm intersect at two points and the length of common chord is 12 cm. Find the distance between their centres.

Q. 101. In a circle with centre O, AB is an arc and C is any point its major arc such that measures of the angles CAO and CBO are 32˚ and 45˚ respectively. Find the measure of the angle subtended by the arc AB at the centre.

Q. 102. AB and CD are two equal chords of a circle whose centre is O. When produced, these chords meet at a point E outside the circle. Prove that : EB= ED.

Q. 103. In an isosceles triangle ABC with AB = AC, a circle passing through B and C intersects the sides AB and AC at D and E respectively. Prove that: (i) DE // BC. (ii) AD × AC = AE × AB.

Q. 104. AC and BD are chords of a circle that bisect each other. Prove that AC and BD are diameters and ABCD is a rectangle.

Q. 105. The bisectors of the opposite angles A and C of a cyclic quadrilateral ABCD intersect the circle at the points E and F respectively. Prove that EF is a diameter of the circle.