Sujeet Kumar

Question 1.Construct ∆ABC such that ∠B =100°, BC = 6.4 cm, ∠C = 50° and construct its incircle.Solution: Steps of construction:i. Construct ∆ABC of the given measurement.ii. Draw the bisectors of ∠B and ∠C. Let these bisectors intersect at point I.iii. Draw a perpendicular IM on side BC. Point M is the foot of the … Read more

Question 1.Radius of circle is 10 cm. There are two chords of length 16 cm each. What will be the distance of these chords from the centre of the circle ?Given: In a circle with centre O,OR and OP are radii and RS and PQ are its congruent chords.PQ = RS= 16 cm,OR = OP … Read more

Question 1.Distance of chord AB from the centre of a circle is 8 cm. Length of the chord AB is 12 cm. Find the diameter of a circle.Given: In a circle with centre O,OA is radius and AB is its chord,seg OP ⊥ chord AB, A-P-BAB = 12 cm, OP =8 cmTo Find: Diameter of … Read more

Question 1.Choose the correct alternative answer and fill in the blanks. i. If all pairs of adjacent sides of a quadrilateral are congruent, then it is called ____.(A) rectangle(B) parallelogram(C) trapezium(D) rhombusAnswer:(D) rhombus ii. If the diagonal of a square is 22√2 cm, then the perimeter of square is ____.(A) 24 cm(B) 24√2 cm(C) 48 … Read more

Question 1.In the adjoining figure, points X, Y, Z are the midpoints of of ∆ABC respectively, cm. Find the lengths of side AB, side BC and side AC AB = 5 cm, AC = 9 cm and BC = 11c.m. Find the lengths of XY, YZ, XZ. Solution: Question 2.In the adjoining figure, □PQRS and … Read more

Question 1.In □IJKL, side IJ || side KL, ∠I = 108° and ∠K = 53°, then find the measures of ∠J and ∠L.Solution: i. ∠I = 108° [Given]side IJ || side KL and side IL is their transveral. [Given]∴ ∠I + ∠L = 180° [Interior angles]∴ 108° + ∠L = 180°∴ ∠L = 180° – … Read more

Question 1.Diagonals of a rectangle ABCD intersect at point O. If AC = 8 cm, then find BO and if ∠CAD = 35°, then find ∠ACB.Solution: i. AC = 8 cm …(i) [Given]□ABCD is a rectangle [Given]∴ BD = AC [Diagonals of a rectangle are congruent]∴ BD = 8 cm [From (i)]∴ BO = 4 … Read more

Question 1.In the adjoining figure, □ABCD is a parallelogram, P and Q are midpoints of sides AB and DC respectively, then prove □APCQ is a parallelogram. Given: □ABCD is a parallelogram. P and Q are the midpoints of sides AB and DC respectively.To prove: □APCQ is a parallelogram.Solution:∴ AP = QC ….(iii) [From (i) and … Read more

Question 1.Diagonals of a parallelogram WXYZ intersect each other at point O. If ∠XYZ∠ = 135°, then measure of ∠XWZ and ∠YZW? If l(OY) = 5 cm, then l(WY) = ?Solution: i. ∠XYZ = 135°□WXYZ is a parallelogram.∠XWZ = ∠XYZ∴ ∠XWZ = 135° …..(i) ii. ∠YZW + ∠XYZ = 180° [Adjacent angles of a parallelogram … Read more

Question 1.Construct ∆XYZ, such that XY + XZ = 10.3 cm, YZ = 4.9 cm, ∠XYZ = 45°.Solution: As shown in the rough figure draw segYZ = 4.9cmDraw a ray YT making an angle of 45° with YZTake a point W on ray YT, such that YW= 10.3 cmNow,YX + XW = YW [Y-X-W]∴ YX … Read more