In a ΔABC, BC is extended up to D; ∠ACD = 150°, ∠B = ¼ ∠A. Then ∠B is

Three circle with radius r1, r2 and r3 touching each other and a common tangent passing through them and touching at point P, Q and R and PQ = 12cm. If the distance between circle with radius r1 and circle with radius r2 is 13cm and distance between circle with radius r2 and circle with radius r3 is 10cm then find r1 : r2 : r3.

The tangents drawn at A and B on the circumference of a circle intersect at P. If ∠APB = 30°, then the measure of the ∠PAB is

In a circle of radius 17 cm, two parallel chords of lengths 30 cm and 16 cm are drawn. If both the chords are on the same side of the centre, then the distance between the chords is

If a circle of radius 12 cm is divided into two equal parts by one concentric circle, then radius of inner circle is

In a ΔABC, ∠A = 100°. If BD and CD are internal bisectors of ∠B and ∠C respectively, then the ∠BDC is,

In ΔABC, ∠B = 35°, ∠C = 65° and the bisector AD of ∠BAC meets BC at D. Then, which of the following is true?

Length and breadth of a rectangle are 8 cm and 6 cm respectively. The rectangle is cut on its four vertices such that the resulting figure is a regular octagon. What is the side (in cm) of the octagon?

Chords AB and CD of a circle intersect at E and are perpendicular to each other. Segments AE, EB and ED are of length 2 cm, 6 cm and 3 cm respectively. Then the length of the diameter of the circle in cm is

Two equal arcs of two circles subtend angle of 60° and 75° at the centre. The ratio of the radii of two circles is

∠A, ∠B, ∠C are three angles of a triangle. If ∠A - ∠B = 18°, ∠B - ∠C = 30°, then ∠A, ∠B and ∠C are

What is the x-intercept of line joining (4, 2) and (6, 3)?

The ratio of in-radius and circum-radius of a square is:

A right angled triangle ABC with right angled at C and the length of the perpendicular from C on AB is p. If the lengths of the sides BC, CA and AB are a, b and c respectively, then which among the following is true?

D, E, F are the mid - points of the sides BC, CA and AB respectively of a ΔABC. Then the ratio of the areas of DEF and ΔABC is D, E, F.

In the given figure, PQ is a diameter of the semicircle PABQ and O is the centre. ∠AOB = 64°. BP cuts AQ at X. What is the value (in degrees) of ∠AXP?

In a triangle, if three altitudes are equal, then the triangle is

O is the center of circle and ∠QPS = 65°. Find the value of ∠A and ∠B respectively.

In the given figure, PQRSTU is a regular hexagon of side 12 cm. What is the area (in cm2) of ΔSQU?

The angles of a triangle are (3x)°,(2x – 7)° and (4x – 11)°. The value of x is

In ∆ABC, the medians AD and BE meet at G. The ratio of the areas of ∆BDG and the quadrilateral GDCE is

ABC is a triangle and its side AB, BC and CA are produced to E, F and G respectively. If ∠CBE = ∠ACF = 130°. Find ∠GAB.

I and O are respectively the in-centre and circumcentre of a triangle ABC. The line AI produced intersects the circumcircle of Δ ABC at the point D. If ∠ABC = x°, ∠BID = y° and ∠BOD = z° , then \(\frac{{z + x}}{y} =\)

In a rectangle,

The lengths of the diagonals of a parallelogram are 10√3 cm and 10√2 cm. If one side of the parallelogram is 13 cm, find the perimeter of the parallelogram.

A chord AB of a circle C1 of radius (√3 + 1) cm touches a circle C2 which is concentric to C1. If the radius of C2 is (√3 - 1) cm, the length of AB is:

In a triangle ABC, sides AB and AC are extended to points D and E respectively, outside the triangle. The bisectors of the exterior angles ∠ECB and ∠DBC meet at a point J. In terms of ∠A, ∠J can be written as

ABC is a triangle in which ∠ABC = 90°. BD is perpendicular to AC. Which of the following is TRUE? I. Triangle BAD is similar to triangle CBD. II. Triangle BAD is similar to triangle CAB. III. Triangle CBD is similar to triangle CAB.

The pair of equations are 7x + 8ky - 16 = 0 and 14x + 112y - 21 = 0. Find the value of ‘k’ for which the system is inconsistent.

If the arcs of same length in two circles subtend angles of 60° and 75° at their centres, the ratio of their radii is