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Geometry 2013-2014 SSC (English Medium) Class 10th Board Exam Question Paper Solution

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Geometry
2013-2014 March
Marks: 40

[5]1 | Solve any five sub-questions:
[1]1.1

In the following figure RP: PK= 3:2, then find the value of A(ΔTRP):A(ΔTPK).

Concept: Properties of Ratios of Areas of Two Triangles
Chapter: [1] Similarity
[1]1.2

If two circles with radii 8 cm and 3 cm, respectively, touch internally, then find the distance between their centers.

Concept: Touching Circles
Chapter: [3] Circle
[1]1.3

If the angle θ = -60° , find the value of sinθ .

Concept: Trigonometric Ratios of Complementary Angles
Chapter: [6] Trigonometry
[1]1.4

Find the slope of the line passing through the points A(2,3) and B(4,7).

Concept: Slope of a Line
Chapter: [4] Co-ordinate Geometry
[1]1.5

The radius of a circle is 7 cm. find the circumference of the circle.

Concept: Problems Based on Areas and Perimeter Or Circumference of Circle, Sector and Segment of a Circle
Chapter: [7] Mensuration
[1]1.6

If the sides of a triangle are 6 cm, 8 cm and 10 cm, respectively, then determine whether the triangle is a right angle triangle or not.

Concept: Pythagoras Theorem
Chapter: [2] Pythagoras Theorem
[8]2 | Solve any four sub-questions:
[2]2.1

In the figure given below, Ray PT is bisector of ∠QPR. If PQ = 5.6 cm, QT = 4 cm and TR = 5 cm, find the value of x .

Concept: Similarity of Triangles
Chapter: [1] Similarity
[2]2.2

In the following figure, Q is the center of the circle. PM and PN are tangents to the circle. If ∠MPN = 40° , find ∠MQN.

 

Concept: Number of Tangents from a Point on a Circle
Chapter: [3] Circle
[2]2.3

Write the equation 2x - 3y - 4 = 0 in the slope intercept form. Hence, write the slope and y-intercept of the line.

Concept: Intercepts Made by a Line
Chapter: [4] Co-ordinate Geometry
[2]2.4

If `cosθ=1/sqrt(2)`, where θ is an acute angle, then find the value of sinθ.

Concept: Trigonometric Ratios of Complementary Angles
Chapter: [6] Trigonometry
[2]2.5

If (4,-3) is a point on the line AB and slope of the line is (-2), write the equation of the line AB.

Concept: General Equation of a Line
Chapter: [4] Co-ordinate Geometry
[2]2.6

Draw a tangent at any point ‘P’ on the circle of radius 3.5 cm and centre O.

Concept: Construction of Tangent to the Circle from the Point on the Circle
Chapter: [5] Geometric Constructions
[9]3 | Solve any three sub-questions:
[3]3.1

In a triangle ABC, line l || Side BC and line l intersects side AB and AC in points P and Q, respectively. Prove that: `"AP"/"BP"="AQ"/"QC"`

Concept: Similarity of Triangles
Chapter: [1] Similarity
[3]3.2

In figure, ΔABC is an isosceles triangle with perimeter 44 cm. The base BC is of length 12 cm. Side AB and side AC are congruent. A circle touches the three sides as shown in the figure below. Find the length of the tangent segment from A to the circle.

Concept: Problems Based on Areas and Perimeter Or Circumference of Circle, Sector and Segment of a Circle
Chapter: [7] Mensuration
[3]3.3

Draw tangents to the circle with center ‘C’ and radius 3.6 cm, from a point B at a distance of 7.2 cm from the center of the circle.

Concept: Construction of Tangents to a Circle
Chapter: [5] Geometric Constructions
[3]3.4

Prove that:

sec2θ + cosec2θ = sec2θ x cosec2θ

Concept: Trigonometric Identities
Chapter: [6] Trigonometry
[3]3.5

Write the equation of each of the following lines:

  1. The x-axis and the y-axis.
  2. The line passing through the origin and the point (-3, 5).
  3. The line passing through the point (-3, 4) and parallel to X-axis.
Concept: General Equation of a Line
Chapter: [4] Co-ordinate Geometry
[8]4 | Solve any two sub-questions:
[4]4.1

From the top of a lighthouse, an observer looks at a ship and finds the angle of depression to be 60° . If the height of the lighthouse is 90 meters, then find how far is that ship from the lighthouse? (√3 = 1.73)

Concept: Heights and Distances
Chapter: [6] Trigonometry
[4]4.2

Prove that the “the opposite angles of the cyclic quadrilateral are supplementary”.

Concept: Cyclic Properties
Chapter: [3] Circle
[4]4.3

The sum of length, breadth and height of a cuboid is 38 cm and the length of its diagonal is 22 cm. Find the total surface area of the cuboid.

Concept: Surface Area of a Combination of Solids
Chapter: [7] Mensuration
[10]5 | Solve any two sub-questions:
[5]5.1

In triangle ABC, ∠C=90°. Let BC= a, CA= b, AB= c and let 'p' be the length of the perpendicular from 'C' on AB, prove that:

1. cp = ab

2. `1/p^2=1/a^2+1/b^2`

 

Concept: Pythagoras Theorem
Chapter: [2] Pythagoras Theorem
[5]5.2

Construct the circumcircle and incircle of an equilateral triangle ABC with side 6 cm and centre O. Find the ratio of radii of circumcircle and incircle.

Concept: Division of a Line Segment
Chapter: [5] Geometric Constructions
[5]5.3

There are three stair-steps as shown in the figure below. Each stair step has width 25 cm, height 12 cm and length 50 cm. How many bricks have been used in it, if each brick is 12.5 cm x 6.25 cm x 4 cm?

Concept: Heights and Distances
Chapter: [6] Trigonometry

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