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

Two poles of height 9m and 14m stand on a plane ground. If the distance between their 12m, find the distance between their tops.

The length of the diagonals of rhombus are 24cm and 10cm. Find each side of the rhombus.

Each side of rhombus is 10cm. If one of its diagonals is 16cm, find the length of the other diagonals.

In ΔABC, AD is perpendicular to BC. Prove that: AB² + CD² = AC² + BD²

In an equilateral triangle ABC, the side BC is trisected at D. Prove that 9 AD² = 7 AB².

From a point O in the interior of aΔABC, perpendicular OD, OE and OF are drawn to the sides BC, CA and AB respectively. Prove that: AF² + BD² + CE² = OA² + OB² + OC² - OD² - OE² - OF²

From a point O in the interior of aΔABC, perpendicular OD, OE and OF are drawn to the sides BC, CA and AB respectively. Prove that: AF² + BD² + CE² = AE² + CD² + BF²

In a triangle ABC, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AC² = AD² + BC x DE + `(1)/(4)"BC"^2`

In a triangle ABC, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AB² = AD² - BC x CE + `(1)/(4)"BC"^2`

In a triangle ABC, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AB² + AC² = 2AD² + `(1)/(2)"BC"^2`

In a triangle ABC, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AC² - AB² = 2BC x ED

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.