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

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°

Evaluate.
sin(90° - A) cosA + cos(90° - A) sinA

Evaluate.
sin²35° + sin²55°

Evaluate.
`cot54^@/(tan36^@)+tan20^@/(cot70^@)-2`

Evaluate.
`(2tan53^@)/(cot37^@)-cot80^@/tan10^@`

Evaluate.
cos²25° + cos²65° - tan²45°

Evaluate.
`(cos^2 32^@+cos^2 58^@)/(sin^2 59^@+sin^2 31^@)`