English Medium Class 9 - CBSE Question Bank Solutions

If the perpendicular bisector of a chord AB of a circle PXAQBY intersects the circle at P and Q, prove that arc PXA ≅ arc PYB.

A, B and C are three points on a circle. Prove that the perpendicular bisectors of AB, BC and CA are concurrent.

If BM and CN are the perpendiculars drawn on the sides AC and AB of the triangle ABC, prove that the points B, C, M and N are concyclic.

Two circles with centres O and O′ intersect at two points A and B. A line PQ is drawn parallel to OO′ through A(or B) intersecting the circles at P and Q. Prove that PQ = 2 OO′.

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

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 ______.

The construction of a triangle ABC, given that BC = 3 cm, ∠C = 60° is possible when difference of AB and AC is equal to ______.

An angle of 52.5° can be constructed.

An angle of 42.5° can be constructed.

A triangle ABC can be constructed in which AB = 5 cm, ∠A = 45° and BC + AC = 5 cm.

A triangle ABC can be constructed in which BC = 6 cm, ∠C = 30° and AC – AB = 4 cm.

A triangle ABC can be constructed in which ∠B = 105°, ∠C = 90° and AB + BC + AC = 10 cm.

A triangle ABC can be constructed in which ∠B = 60°, ∠C = 45° and AB + BC + AC = 12 cm.

Construct a triangle whose sides are 3.6 cm, 3.0 cm and 4.8 cm. Bisect the smallest angle and measure each part.

Construct a triangle ABC in which BC = 5 cm, ∠B = 60° and AC + AB = 7.5 cm.

Construct the following and give justification:

A triangle PQR given that QR = 3 cm, ∠PQR = 45° and QP – PR = 2 cm.

Construct the following and give justification:

A right triangle when one side is 3.5 cm and sum of other sides and the hypotenuse is 5.5 cm.

Construct the following and give justification:

An equilateral triangle if its altitude is 3.2 cm.

Construct the following and give justification:

A rhombus whose diagonals are 4 cm and 6 cm in lengths.

The perimeter of an equilateral triangle is 60 m. The area is ______.