English Medium Class 9 - CBSE Question Bank Solutions

In the following figure, the area of parallelogram ABCD is ______.

AD is a diameter of a circle and AB is a chord. If AD = 34 cm, AB = 30 cm, the distance of AB from the centre of the circle is ______.

In the following figure, if OA = 5 cm, AB = 8 cm and OD is perpendicular to AB, then CD is equal to ______.

If AB = 12 cm, BC = 16 cm and AB is perpendicular to BC, then the radius of the circle passing through the points A, B and C is ______.

In the following figure, if ∠ABC = 20º, then ∠AOC is equal to ______.

In the following figure, if AOB is a diameter of the circle and AC = BC, then ∠CAB is equal to ______.

In the following figure, if ∠OAB = 40º, then ∠ACB is equal to ______.

In the following figure, if ∠DAB = 60º, ∠ABD = 50º, then ∠ACB is equal to ______.

In the following figure, BC is a diameter of the circle and ∠BAO = 60º. Then ∠ADC is equal to ______.

In the following figure, ∠AOB = 90º and ∠ABC = 30º, then ∠CAO is equal to ______.

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.