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Construct a triangle whose sides are 3.6 cm, 3.0 cm and 4.8 cm. Bisect the smallest angle and measure each part.

Solution According to the given details We have to construct a triangle whose sides are 3.6 cm, 3.0 cm and 4.8 cm. And to bisect the... View Article

Draw an angle of 80° with the help of a protractor. Then construct angles of (i) 40° (ii)160° (iii) 120°.

Solution According to the given details We have to draw an angle of 80° with the help of a protractor. Then construct angles of (i)... View Article

Draw a line segment AB of 4 cm in length. Draw a line perpendicular to AB through A and B, respectively. Are these lines parallel?

Solution According to the given details A line segment AB of length 4cm. To draw a perpendicular to AB through A and B, respectively. The... View Article

Draw an angle of 110° with the help of a protractor and bisect it. Measure each angle.

Solution According to the given details An angle ABC = 110o and to draw the bisector of ∠ABC The steps of construction for an... View Article

A triangle ABC can be constructed in which AB = 5 cm, ∠A = 45° and BC + AC = 5 cm. Write True or False in each of the following. Give reasons for your answer.

The given statement is True Explanation We know that the Sum of any two sides of a triangle must be greater than the third side. So as per the... View Article

An angle of 42.5° can be constructed. Write True or False in each of the following. Give reasons for your answer.

The given statement is False Explanation We know that, 42.5° = 1/2 x 85° An angle of 85° cannot be constructed with... View Article

An angle of 52.5° can be constructed. Write True or False in each of the following. Give reasons for your answer.

The given statement is True Explanation An angle of 52.5°can be constructed by bisecting angle 105° 52.5° = ½... View Article

With the help of a ruler and a compass it is not possible to construct an angle of : (A) 37.5° (B) 40° (C) 22.5° (D) 67.5°

The correct answer is (B) 40° Solution With the help of a ruler and a compass, we can construct the angels, 90°, 60°, 45°,... View Article

Prove that angle bisector of any angle of a triangle and perpendicular bisector of the opposite side if intersect, they will intersect on the circumcircle of the triangle.

Given According to the given details Triangle ABC and l is the perpendicular bisector of BC. To Prove Angles bisector of ∠A and... View Article

ABCD is a parallelogram. A circle through A, B is so drawn that it intersects AD at P and BC at Q. Prove that P, Q, C and D are concyclic.

Given ABCD is a parallelogram. A circle through A, B is so drawn that it intersects AD at P and BC at Q. To Prove P, Q, C and D are... View Article

If P, Q and R are the mid-points of the sides BC, CA and AB of a triangle and AD is the perpendicular from A on BC, prove that P, Q, R and D are concyclic.

Given According to the given details P, Q and R are the mid-points of the sides BC, CA and AB of a triangle and AD is the... View Article

If non-parallel sides of a trapezium are equal, prove that it is cyclic.

Given According to the given details ABCD is a trapezium in which AD||BC Non-parallel sides AB and DC of the trapezium ABCD are equal... View Article

If two equal chords of a circle intersect, prove that the parts of one chord are separately equal to the parts of the other chord.

Given According to the given details AB and CD are two equal chords of a circle with centre O, intersect each other at M. To Prove (i)... View Article

If BM and CN are the perpendiculars drawn on the sides AC and AB of the triangle ABC, prove that the points B, C, M and N are concyclic.

Given According to the given details BM and CN are the perpendiculars drawn on the sides AC and AB of the triangle ABC. To Prove We have... View Article

Two chords AB and AC of a circle subtends angles equal to 90º and 150º, respectively at the centre. Find ∠BAC, if AB and AC lie on the opposite sides of the centre.

Given According to the given details ∠AOC=90º and∠AOB= 150º Find out We have to determine ∠BAC,... View Article

On a common hypotenuse AB, two right triangles ACB and ADB are situated on opposite sides. Prove that ∠BAC = ∠BDC.

Given According to the given details ACB and ADB are two right triangles. To Prove We have to prove that ∠BAC = ∠BDC Proof... View Article

O is the circumcentre of the triangle ABC and D is the mid-point of the base BC. Prove that ∠BOD = ∠A.

Given According to the given details O is the circumcenter of the triangle ABC and D is the midpoint of BC. To Prove We have to prove... View Article

ABCD is such a quadrilateral that A is the centre of the circle passing through B, C and D. Prove that ∠CBD + ∠CDB = 1/2 ∠BAD

Given According to the given details A quadrilateral ABCD such that A is the centre of the circle passing through B, C and D. To Prove... View Article

If a line segment joining mid-points of two chords of a circle passes through the centre of the circle, prove that the two chords are parallel.

Given According to the given details AB and CD to be the chords of the circle with centre O. To Prove We have to prove that... View Article

AB and AC are two equal chords of a circle. Prove that the bisector of the angle BAC passes through the centre of the circle.

Given According to the given details AB and AC are two chords that are equal with centre O. AM is the bisector of ∠BAC. To Prove We... View Article

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