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In Figure a square is inscribed in a circle of diameter d and another square is circumscribing the circle. Is the area of the outer square four times the area of the inner square? Give reasons for your answer.

Answer The given statement is False Solution Let us assume the diameter of the circle = d Therefore, Diagonal of... View Article

Will it be true to say that the perimeter of a square circumscribing a circle of radius a cm is 8a cm? Give reasons for your answer.

The given statement is True Solution Let us assume the radius of circle = a cm ∴ Diameter of the circle =... View Article

Is the area of the circle inscribed in a square of side a cm, a2 cm2? Give reasons for your answer.

The given statement is False Solution Let us assume the side of square to be S. Given that the circle is... View Article

If the perimeter of a circle is equal to that of a square, then the ratio of their areas is (A) 22 : 7 (B) 14 : 11 (C) 7 : 22 (D) 11: 14

The correct answer is (B) 14 : 11 Solution Let r be the radius of the circle and a be the... View Article

Area of the largest triangle that can be inscribed in a semi-circle of radius r units is (A) r² sq. units (B) 1/2 r² sq. units (C) 2 r² sq. units (D) √2 r² sq. units

The correct answer is (A) r2 sq. units Solution The largest triangle that can be inscribed in a semi-circle of radius r... View Article

If the circumference of a circle and the perimeter of a square are equal, then (A) Area of the circle = Area of the square (B) Area of the circle > Area of the square (C) Area of the circle < Area of the square (D) Nothing definite can be said about the relation between the areas of the circle & square.

The correct answer is (B) Area of the circle > Area of the square Solution According to the given parameters Circumference... View Article

If the sum of the circumferences of two circles with radii R₁ and R₂ is equal to the circumference of a circle of radius R, then (A) R₁ + R₂ = R (B) R₁ + R₂ > R (C) R₁ + R₂ < R (D) Nothing definite can be said about the relation among R₁, R₂ & R.

The correct answer is (A) R1 + R2 = R Solution According to the given parameters Circumference of circle with radius R =... View Article

If the sum of the areas of two circles with radii R₁ and R₂ is equal to the area of a circle of radius R, then (A) R₁ + R₂ = R (B) R₁₂ + R₂₂ = R₂ (C) R₁ + R₂< R (D) R₁₂ + R₂₂ < R₂

The correct answer is (B) R12 + R22 = R2 Solution According to the given parameters Area of circle = Area of first circle... View Article

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.... 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... 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 =... 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... 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... 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... 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... 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... 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... 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... 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

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