English Medium इयत्ता ९ - CBSE Question Bank Solutions

The lengths of two parallel chords of a circle are 6 cm and 8 cm. if the smaller chord is at a distance of 4 cm from the centre, what is the distance of the other chord from the centre?

Three girls Ishita, Isha and Nisha are playing a game by standing on a circle of radius 20 m drawn in a park. Ishita throws a ball o Isha, Isha to Nisha and Nisha to Ishita. If the distance between Ishita and Isha and between Isha and Nisha is 24 m each, what is the distance between Ishita and Nisha.

In the below fig. ABCD and AEFD are two parallelograms. Prove that
(1) PE = FQ
(2) ar (Δ APE) : ar (ΔPFA) = ar Δ(QFD) : ar (Δ PFD)
(3) ar (ΔPEA) = ar (ΔQFD)

In Fig. 10.40, it is given that RT = TS, ∠1 = 2∠2 and ∠4 = 2∠3. Prove that ΔRBT ≅ ΔSAT. 

In Fig. 10.92, it is given that AB = CD and AD = BC. Prove that ΔADC ≅ ΔCBA. 

If perpendiculars from any point within an angle on its arms are congruent, prove that it lies on the bisector of that angle.  

In Fig. 10.99, AD ⊥ CD and CB ⊥. CD. If AQ = BP and DP = CQ, prove that ∠DAQ = ∠CBP. 

ABCD is a square, X and Yare points on sides AD and BC respectively such that AY = BX. Prove that BY = AX and ∠BAY = ∠ABX. 

Construct a ΔABC in which BC = 3.6 cm, AB + AC = 4.8 cm and ∠B = 60°.

Construct a ΔABC in which AB + AC = 5.6 cm, BC = 4.5 cm, AB − AC = 1.5 cm and ∠B = 45°.

Construct a ΔABC in which BC = 3.4 cm, AB − AC = 1.5 cm and ∠B = 45°.

Using ruler and compasses only, construct a ΔABC, given base BC = 7cm, ∠ABC = 60° and AB + AC = 12 cm.

Construct a triangle whose perimeter is 6.4 cm, and angles at the base are 60° and 45° .

Using ruler and compasses only, construct a ΔABC from the following data:
AB + BC + CA = 12 cm, ∠B = 45° and ∠C = 60°.

Construct a right triangle ABC whose base BC is 6 cm and the sum of hypotenuse AC and other side AB is 10 cm.

Construct a right-angled triangle whose perimeter is equal to 10 cm and one acute angle equal to 60°.

Construct a triangle ABC such that BC = 6 cm, AB = 6 cm and median AD = 4 cm.

Construct a triangle XYZ in which ∠Y = 30°, ∠Z = 90° and XY + YZ + ZX = 11.

Which of the following numbers can be represented as non-terminating, repeating decimals?

Plot the following point on the graph paper:

(2, 5)