English Medium Class 9 - 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 distance 4 cm from the centre, what is the distance of the other chord from the centre?

Bisectors of angles A, B and C of a triangle ABC intersect its circumcircle at D, E and F respectively. Prove that the angles of the triangle DEF are 90°-A, 90° − `1/2 A, 90° − 1/2 B, 90° − 1/2` C.

In a ΔABC, if ∠A=l20° and AB = AC. Find ∠B and ∠C. 

In Figure AB = AC and ∠ACD =105°, find ∠BAC.  

Find the measure of each exterior angle of an equilateral triangle. 

If the base of an isosceles triangle is produced on both sides, prove that the exterior angles so formed are equal to each other. 

In figure, AB = AC and DB = DC, find the ratio ∠ABD : ∠ACD 

Determine the measure of each of the equal angles of a right-angled isosceles triangle.

AB is a line seg P and Q are points on opposite sides of AB such that each of them is equidistant from the points A and B (See Fig. 10.26). Show that the line PQ is perpendicular bisector of AB. 

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

Two lines AB and CD intersect at O such that BC is equal and parallel to AD. Prove that the lines AB and CD bisect at O.

In Fig. 10.23, PQRS is a square and SRT is an equilateral triangle. Prove that
(i) PT = QT (ii) ∠TQR = 15° 

Prove that the medians of an equilateral triangle are equal. 

In a ΔABC, if ∠A=l20° and AB = AC. Find ∠B and ∠C. 

In a ΔABC, if AB = AC and ∠B = 70°, find ∠A. 

The vertical angle of an isosceles triangle is 100°. Find its base angles. 

In Figure 10.24, AB = AC and ∠ACD =105°, find ∠BAC. 

Find the measure of each exterior angle of an equilateral triangle. 

If the base of an isosceles triangle is produced on both sides, prove that the exterior angles so formed are equal to each other. 

Two lines AB and CD intersect at O such that BC is equal and parallel to AD. Prove that the lines AB and CD bisect at O.