English Medium कक्षा ९ - CBSE Question Bank Solutions

A circle of radius 3 cm can be drawn through two points A, B such that AB = 6 cm.

If AOB is a diameter of a circle and C is a point on the circle, then AC² + BC² = AB².

If A, B, C, D are four points such that ∠BAC = 30° and ∠BDC = 60°, then D is the centre of the circle through A, B and C.

If A, B, C and D are four points such that ∠BAC = 45° and ∠BDC = 45°, then A, B, C, D are concyclic.

In the following figure, if AOB is a diameter and ∠ADC = 120°, then ∠CAB = 30°.

AB and AC are two equal chords of a circle. Prove that the bisector of the angle BAC passes through the centre of the circle.

If a line segment joining mid-points of two chords of a circle passes through the centre of the circle, prove that the two chords are parallel.

O is the circumcentre of the triangle ABC and D is the mid-point of the base BC. Prove that ∠BOD = ∠A.

On a common hypotenuse AB, two right triangles ACB and ADB are situated on opposite sides. Prove that ∠BAC = ∠BDC.

Two chords AB and AC of a circle subtends angles equal to 90º and 150º, respectively at the centre. Find ∠BAC, if AB and AC lie on the opposite sides of the centre.

The circumcentre of the triangle ABC is O. Prove that ∠OBC + ∠BAC = 90º.

In the following figure, ∠ADC = 130° and chord BC = chord BE. Find ∠CBE.

A quadrilateral ABCD is inscribed in a circle such that AB is a diameter and ∠ADC = 130º. Find ∠BAC.

In the following figure, ∠OAB = 30º and ∠OCB = 57º. Find ∠BOC and ∠AOC.

Prove that angle bisector of any angle of a triangle and perpendicular bisector of the opposite side if intersect, they will intersect on the circumcircle of the triangle.

If two chords AB and CD of a circle AYDZBWCX intersect at right angles (see figure), prove that arc CXA + arc DZB = arc AYD + arc BWC = semi-circle.

If ABC is an equilateral triangle inscribed in a circle and P be any point on the minor arc BC which does not coincide with B or C, prove that PA is angle bisector of ∠BPC.

In the following figure, O is the centre of the circle, ∠BCO = 30°. Find x and y.

In the following figure, O is the centre of the circle, BD = OD and CD ⊥ AB. Find ∠CAB.

The total surface area of a cube is 96 cm². The volume of the cube is ______.