(English Medium) ICSE Class 9 - CISCE Question Bank Solutions for Mathematics

In a triangle ABC, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AB² + AC² = 2(AD² + CD²)

A point OI in the interior of a rectangle ABCD is joined with each of the vertices A, B, C and D. Prove that  OB² + OD² = OC² + OA²

AD is perpendicular to the side BC of an equilateral ΔABC. Prove that 4AD² = 3AB².

In a triangle ABC right angled at C, P and Q are points of sides CA and CB respectively, which divide these sides the ratio 2 : 1.
Prove that: 9AQ² = 9AC² + 4BC² 

In a triangle ABC right angled at C, P and Q are points of sides CA and CB respectively, which divide these sides the ratio 2 : 1.
Prove that: 9BP² = 9BC² + 4AC²

In a triangle ABC right angled at C, P and Q are points of sides CA and CB respectively, which divide these sides the ratio 2 : 1.
Prove that : 9(AQ² + BP²) = 13AB² 

In the given figure, PQ = `"RS"/(3)` = 8cm, 3ST = 4QT = 48cm.
SHow that ∠RTP = 90°.

In a right-angled triangle ABC,ABC = 90°, AC = 10 cm, BC = 6 cm and BC produced to D such CD = 9 cm. Find the length of AD.

In the given figure. PQ = PS, P =R = 90°. RS = 20 cm and QR = 21 cm. Find the length of PQ correct to two decimal places.

In a right-angled triangle PQR, right-angled at Q, S and T are points on PQ and QR respectively such as PT = SR = 13 cm, QT = 5 cm and PS = TR. Find the length of PQ and PS.

PQR is an isosceles triangle with PQ = PR = 10 cm and QR = 12 cm. Find the length of the perpendicular from P to QR.

In a square PQRS of side 5 cm, A, B, C and D are points on sides PQ, QR, RS and SP respectively such as PA = PD = RB = RC = 2 cm. Prove that ABCD is a rectangle. Also, find the area and perimeter of the rectangle.

Define primary data and secondary data.

Explain the meaning of the following terms: Variate

Explain the meaning of the following terms: Class mark

Explain the meaning of the following terms: True Class Limits

Explain the meaning of the following terms: Frequency

Construct a quadrilateral ABCD in which
AB = 4.6cm, BD = 5cm, AC = 6cm, CD = 4.2cm and ∠A = 90°

Construct a quadrilateral ABCD in which
AB = 7.2cm, BC = 5.8cm, CD = 6.3cm, AD = 4.3cm and ∠A = 75° 

Construct a quadrilateral ABCD in which
AB = 4.8cm, AC = 5.8cm, AD = 3.6cm, ∠A = 105° and ∠B = 60°