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Draw two concentric circles of radii 3 cm and 5 cm. Taking a point on outer circle construct the pair of tangents to the other. Measure the length of a tangent and verify it by actual calculation.

Given Two concentric circles of radii 3 cm and 5 cm Solution Listed below are the steps of construction 1. Draw a circle with centre O and... View Article

Draw a parallelogram ABCD in which BC = 5 cm, AB = 3 cm and angle ABC = 60°, divide it into triangles BCD and ABD by the diagonal BD. Construct the triangle BD‘ C‘ similar to triangle BDC with scale factor 4/3. Draw the line segment D‘A‘ parallel to DA where A’ lies on extended side BA. Is A’BC’D’ a parallelogram?

Given A parallelogram ABCD in which BC = 5 cm, AB = 3 cm and angle ABC = 60° Find out We have to determine if A’BC’D’ is... View Article

Two line segments AB and AC include an angle of 60° where AB = 5 cm and AC = 7 cm. Locate points P and Q on AB and AC, respectively such that AP = 3/4 AB and AQ = 1/4 AC. Join P and Q and measure the length PQ.

Given Two line segments AB and AC include an angle of 60° where AB = 5 cm and AC = 7 cm Find out We have to determine the the length PQ... View Article

Draw a right triangle ABC in which BC = 12 cm, AB = 5 cm and ∠B = 90°. Construct a triangle similar to it and of scale factor 2/3. Is the new triangle also a right triangle?

Given A right triangle ABC in which BC = 12 cm, AB = 5 cm and ∠B = 90 Find out We have to determine the new triangle formed... View Article

Draw a line segment of length 7 cm. Find a point P on it which divides it in the ratio 3:5.

Given A line segment of length 7 cm Find out We have to determine the point P on it which divides it in the ratio of 3:5 Solution... View Article

To construct a triangle similar to a given △ABC with its sides 7/3 of the corresponding sides of △ABC, draw a ray BX making acute angle with BC and X lies on the opposite side of A with respect to BC. The points B₁, B₂, …., B₇ are located at equal distances on BX, B₃ is joined to C and then a line segment B₆C‘ is drawn parallel to B₃C where C‘ lies on BC produced. Finally, line segment A‘C‘ is drawn parallel to AC. Write True or False and give reasons for your answer.

The correct answer is False Solution Let us first construct as per the given parameters. Listed below are the steps of construction 1. Draw... View Article

By geometrical construction, it is possible to divide a line segment in the ratio √3:(1/√3) Write True or False and give reasons for your answer.

The correct answer is True Solution According to the given details, we know that Ratio= √3 : ( 1/√3) On simplifying we... View Article

To divide a line segment AB in the ratio 5 : 6, draw a ray AX such that ∠BAX is an acute angle, then draw a ray BY parallel to AX and the points A₁, A₂, A₃, … and B₁, B₂, B₃, … are located at equal distances on ray AX and BY, respectively. Then the points joined are (A) A₅ and B₆ (B) A₆ and B₅ (C) A₄ and B₅ (D) A₅and B₄

The correct answer is (A) A5 and B6 Solution According to the given details, we know that A line segment AB in the ratio 5:7 So, A:B =... View Article

To divide a line segment AB in the ratio 4:7, a ray AX is drawn first such that BAX is an acute angle and then points A₁, A₂, A₃,…. are located at equal distances on the ray AX and the point B is joined to (A) A₁₂(B) A₁₁ (C) A₁₀ (D) A₉

The correct answer is (B) A11 Solution According to the given details, we know that A line segment AB in the ratio 4:7 So, A:B = 4:7... View Article

To divide a line segment AB in the ratio 5:7, first a ray AX is drawn so that BAX is an acute angle and then at equal distances points are marked on the ray AX such that the minimum number of these points is (A) 8 (B) 10 (C) 11 (D) 12

The correct answer is (D) 12 Solution According to the given details, we know that A line segment AB in the ratio 5:7 So, A:B = 5:7... View Article

In Figure tangents PQ and PR are drawn to a circle such that ∠RPQ = 30°. A chord RS is drawn parallel to the tangent PQ. Find the ∠RQS.

Solution: According to the given parameters Tangents PQ and PR are drawn to a circle such that ∠RPQ = 30°. A chord RS is... View Article

In a right triangle ABC in which ∠B = 90°, a circle is drawn with AB as diameter intersecting the hypotenuse AC and P. Prove that the tangent to the circle at P bisects BC.

According to the given parameters In a right angle ΔABC is which ∠B = 90°, a circle is drawn with AB as diameter... View Article

Two circles with centres O and O‘ of radii 3 cm and 4 cm, respectively intersect at two points P and Q such that OP and O‘P are tangents to the two circles. Find the length of the common chord PQ.

According to the given parameters Two circles with centres O and O’ of radii 3 cm and 4 cm, respectively intersect at two points P... View Article

If AB is a chord of a circle with centre O, AOC is a diameter and AT is the tangent at A as shown in Figure. Prove that ∠BAT = ∠ACB

Solution: According to the given parameters A circle with center O and AC as diameter and AB and BC as two chords also AT is a tangent... View Article

From an external point P, two tangents, PA and PB are drawn to a circle with centre O. At one point E on the circle tangent is drawn which intersects PA and PB at C and D, respectively. If PA = 10 cm, find the perimeter of the triangle PCD.

According to the given details From an external point P, two tangents, PA and PB are drawn to a circle with centre O. At a point, E on... View Article

Let s denote the semi-perimeter of a triangle ABC in which BC = a, CA = b, AB = c. If a circle touches the sides BC, CA, AB at D, E, F, respectively, prove that BD = s – b.

According to the given details A triangle ABC with BC = a CA = b AB = c . A circle is inscribed which touches the sides BC, CA... View Article

If from an external point B of a circle with centre O, two tangents BC and BD are drawn such that angle DBC = 120°, prove that BC + BD = BO, i.e., BO = 2BC.

Solution According to the given details and by RHS rule ΔOBC and ΔOBD are congruent By corresponding parts of... View Article

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