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Question Paper Solutions - Geometry 2013 - 2014-S.S.C-10th Maharashtra State Board (MSBSHSE)


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).

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

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

Chapter: [2] Circle
Concept: Touching Circles
[1]1.3

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

Chapter: [5] Trigonometry
Concept: Trigonometric Ratios of Complementary Angles
[1]1.4

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

Chapter: [2.07] Co-ordinate Geometry
Concept: Slope of a Line
[1]1.5

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

Chapter: [6] Mensuration
Concept: Problems Based on Areas and Perimeter Or Circumference of Circle, Sector and Segment of a Circle
[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.

Chapter: [1] Similarity
Concept: 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 .

Chapter: [3.01] Triangles
Concept: Similarity of Triangles
[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.

 

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

Chapter: [3] Co-ordinate Geometry
Concept: Intercepts Made by a Line
[2]2.4

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

Chapter: [5] Trigonometry
Concept: Trigonometric Ratios of Complementary Angles
[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.

Chapter: [3] Co-ordinate Geometry
Concept: General Equation of a Line
[2]2.6

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

Chapter: [4] Geometric Constructions
Concept: Construction of Tangent to the Circle from the Point on the Circle
[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"`

Chapter: [3.01] Triangles
Concept: Similarity of Triangles
[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.

Chapter: [6] Mensuration
Concept: Problems Based on Areas and Perimeter Or Circumference of Circle, Sector and Segment of a Circle
[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.

Chapter: [3.03] Constructions
Concept: Construction of Tangents to a Circle
[3]3.4

Prove that:

sec2θ + cosec2θ = sec2θ x cosec2θ

Chapter: [5] Trigonometry
Concept: Trigonometric Identities
[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.
Chapter: [3] Co-ordinate Geometry
Concept: General Equation of a Line
[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)

Chapter: [4.03] Heights and Distances
Concept: Heights and Distances
[4]4.2

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

Chapter: [3.04] Circles
Concept: Cyclic Properties
[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.

Chapter: [7.02] Surface Areas and Volumes
Concept: Surface Area of a Combination of Solids
[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`

 

Chapter: [1] Similarity
Concept: 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.

Chapter: [4] Geometric Constructions
Concept: Division of a Line Segment
[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?

Chapter: [4.03] Heights and Distances
Concept: Heights and Distances

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