English Medium Class 9 - CBSE Question Bank Solutions for Mathematics

The side BC of ΔABC is produced to a point D. The bisector of ∠A meets side BC in L. If ∠ABC = 30° and ∠ACD = 115°, then ∠ALC = ______.

In the given figure, ∠BAD = 78°, ∠DCF = x° and ∠DEF = y°. Find the values of x and y. 

In the given figure, if l₁ || l₂, the value of x is

In the given figure, ABCD is a cyclic quadrilateral. Find the value of x.

ABCD is a cyclic quadrilateral in  BC || AD, ∠ADC = 110° and ∠BAC = 50°. Find ∠DAC.

ABCD is a cyclic quadrilateral in  ∠DBC = 80° and ∠BAC = 40°. Find ∠BCD.

ABCD is a cyclic quadrilateral in   ∠BCD = 100° and ∠ABD = 70° find ∠ADB.

Prove that the circles described on the four sides of a rhombus as diameters, pass through the point of intersection of its diagonals. 

Circles are described on the sides of a triangle as diameters. Prove that the circles on any two sides intersect each other on the third side (or third side produced).

ABCD is a cyclic trapezium with AD || BC. If ∠B = 70°, determine other three angles of the trapezium.

In the given figure, ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If ∠DBC = 55° and ∠BAC = 45°, find ∠BCD.

Prove that the perpendicular bisectors of the sides of a cyclic quadrilateral are concurrent.

Prove that the centre of the circle circumscribing the cyclic rectangle ABCD is the point of intersection of its diagonals.

ABCD is a cyclic quadrilateral in which BA and CD when produced meet in E and EA = ED. Prove that AD || BC . 

ABCD is a cyclic quadrilateral in which BA and CD when produced meet in E and EA = ED. Prove that  EB = EC. 

In the given figure, ABCD is a cyclic quadrilateral in which ∠BAD = 75°, ∠ABD = 58° and ∠ADC = 77°, AC and BD intersect at P. Then, find ∠DPC.

In the given figure, ABCD is a quadrilateral inscribed in a circle with centre O. CD is produced to E such that ∠AED = 95° and ∠OBA = 30°. Find ∠OAC.

ABCD is a cyclic quadrilateral such that ∠ADB = 30° and ∠DCA = 80°, then ∠DAB =