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Construction

The construction of a triangle ABC, given that BC = 6 cm, ∠B = 45° is not possible when difference of AB and AC is equal to:

(A) 6.9 cm (B) 5.2 cm (C) 5.0 cm (D)4.0 cm

Construction

With the help of a ruler and a compass it is not possible to construct an angle of :

(A) 37.5° (B) 40° (C) 22.5° (D) 67.5°

Construction

The construction of a triangle ABC in which AB = 4 cm, ∠A = 60° is not possible when difference of BC and AC is equal to:

(A) 3.5 cm (B) 4.5 cm (C) 3 cm (D) 2.5 cm

Construction

With the help of a ruler and a compass, it is possible to construct an angle of :

(A) 35° (B) 40° (C) 37.5° (D) 47.5°

Circles

Two equal chords AB and CD of a circle when produced intersect at a point P. Prove that PB = PD.

Circles

If bisectors of opposite angles of a cyclic quadrilateral ABCD intersect the circle, circumscribing it at the points P and Q, prove that PQ is a diameter of the circle

Circles

If ABC is an equilateral triangle inscribed in a circle and P be any point on the minor arc BC which does not coincide with B or C, prove that PA is
angle bisector of ∠BPC.

Circles

Prove that angle bisector of any angle of a triangle and perpendicular bisector of the opposite side if intersect, they will intersect on the circumcircle of the triangle.

Circles

ABCD is a parallelogram. A circle through A, B is so drawn that it intersects AD at P and BC at Q. Prove that P, Q, C and D are concyclic.

Circles

If P, Q and R are the mid-points of the sides BC, CA and AB of a triangle and AD is the perpendicular from A on BC, prove that P, Q, R and D are concyclic.