(English Medium) ICSE Class 10 - CISCE Question Bank Solutions for Mathematics

In the figure, given alongside, AB || CD and O is the centre of the circle. If ∠ADC = 25°; find the angle AEB. Give reasons in support of your answer.

ABCD is a cyclic quadrilateral in which AB is parallel to DC and AB is a diameter of the circle. Given ∠BED = 65°, calculate:

1. ∠DAB,
2. ∠BDC.

In the given figure, AB is a diameter of the circle. Chord ED is parallel to AB and ∠EAB = 63°.

Calculate:

1. ∠EBA,
2. ∠BCD.

In the given figure, PQ is a diameter. Chord SR is parallel to PQ. Given that ∠PQR = 58°,

Calculate:

1. ∠RPQ,
2. ∠STP.

Prove that the perimeter of a right triangle is equal to the sum of the diameter of its incircle and twice the diameter of its circumcircle.

In the following figure, AD is the diameter of the circle with centre O. Chords AB, BC and CD are equal. If ∠DEF = 110°, calculate: ∠AEF

Prove that the circle drawn on any one of the equal sides of an isosceles triangle as diameter bisects the base.

The following figure shows a circle with PR as its diameter. If PQ = 7 cm and QR = 3RS = 6 cm, find the perimeter of the cyclic quadrilateral PQRS.

In the given figure, AB is the diameter of a circle with centre O.

If chord AC = chord AD, prove that:

1. arc BC = arc DB
2. AB is bisector of ∠CAD.

Further, if the length of arc AC is twice the length of arc BC, find:

1. ∠BAC
2. ∠ABC

Solve.
`cos22/sin68`

Solve.
`tan47/cot43`

Solve.
`sec75/(cosec15)`

Solve.
`cos55/sin35+cot35/tan55`

In the figure, given below, AB and CD are two parallel chords and O is the centre. If the radius of the circle is 15 cm, find the distance MN between the two chords of lengths 24 cm and 18 cm respectively.

solve.
cos²40° + cos²50°

solve.
sec² 18° - cot² 72°

Solve.
sin15° cos75° + cos15° sin75°

Solve.
sin42° sin48° - cos42° cos48°