# Geometry Set A 2017-2018 SSC (Marathi Semi-English) 10th Standard [इयत्ता १० वी] Question Paper Solution

Geometry [Set A]
Date & Time: 12th March 2018, 11:00 am
Duration: 2h

[5]1 | Attempt any FIVE of the following sub-questions
[1]1.1

triangleDEF ~ triangleMNK. If DE = 5 and MN = 6, then find the value of (A(triangleDEF))/(A(triangleMNK))

Concept: Similarity of Triangles
Chapter: [0.01] Similarity
[1]1.2

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

Concept: Touching Circles
Chapter: [0.03] Circle
[1]1.3

Find the length of the altitude of an equilateral triangle with side 6 cm.

Concept: Construction of Triangle If the Base, Angle Opposite to It and Either Median Altitude is Given
Chapter: [0.05] Geometric Constructions
[1]1.4

If theta = 45^@, then find tan theta.

Concept: Angles in Standard Position
Chapter: [0.06] Trigonometry
[1]1.5

A slope of a line is 3 and y-intercept is –4. Write the equation of a line

Concept: Slope of a Line
Chapter: [0.04] Co-ordinate Geometry
[1]1.6

Using Euler’s formula, find V if E = 30, F = 12.

Concept: Euler's Formula
Chapter: [0.07] Mensuration
[8]2 | Attempt any FOUR of the following subquestions:
[2]2.1

The ratio of the areas of two triangles with common base is 6:5. Height of the larger triangle of 9 cm, then find the corresponding height of the smaller triangle.

Concept: Properties of Ratios of Areas of Two Triangles
Chapter: [0.01] Similarity
[2]2.2

In the following figure, point ‘A’ is the centre of the circle. Line MN is tangent at point M. If AN = 10 cm and MN = 5 cm, determine radius of the circle.

Concept: Theorem - Converse of Tangent at Any Point to the Circle is Perpendicular to the Radius
Chapter: [0.03] Circle
[2]2.3

Draw angle ABC of measure 80° and bisect it

Concept: Basic Geometric Constructions
Chapter: [0.05] Geometric Constructions
[2]2.4

if cos theta = 5/13 where theta is an acute angle. Find the value of sin theta

Concept: Trigonometric Identities
Chapter: [0.06] Trigonometry
[2]2.5

The volume of a cube is 512 cm3. Find its side.

Concept: Surface Area of a Combination of Solids
Chapter: [0.07] Mensuration
[2]2.6

The radius and slant height of a cone are 5 cm and 20 cm respectively. Find its curved surface area. (Π = 3.14)

Concept: Surface Area of a Combination of Solids
Chapter: [0.07] Mensuration
[9]3 | Attempt any THREE of the following subquestions
[3]3.1

In the following figure, seg DH ⊥ seg EF and seg GK ⊥ seg EF. If DH = 18 cm, GK = 30 cm and A(triangle DEF) = 450 cm^2, then find:

1) EF

2) A(triangle GFE)

3) A(square DFGE)

Concept: Similarity of Triangles
Chapter: [0.01] Similarity
[3]3.2

In the following figure, ray PA is a tangent to the circle at A and PBC is a secant. If AP = 15, BP = 10, then find BC.

Concept: Tangent - Secant Theorem
Chapter: [0.03] Circle
[3]3.3

Draw the circle with centre C and radius 3.5 cm. Point B is at a distance 7 cm from the centre. Draw tangents to the circle from the point B.

Concept: Construction of Tangent to the Circle from the Point on the Circle
Chapter: [0.05] Geometric Constructions
[3]3.4

Show that sqrt((1+cosA)/(1-cosA)) = cosec A + cot A

Concept: Trigonometric Identities
Chapter: [0.06] Trigonometry
[3]3.5

Write the equation of the line passing through A(–3, 4) and B(4, 5) in the form of ax + by + c = 0

Concept: Standard Forms of Equation of a Line
Chapter: [0.04] Co-ordinate Geometry
[8]4 | Attempt any TWO of the following subquestions
[4]4.1

Prove that “The lengths of the two tangent segments to a circle drawn from an external point are equal.”

Concept: Number of Tangents from a Point on a Circle
Chapter: [0.03] Circle [0.03] Circle
[4]4.2

A tree is broken by the wind. The top of that tree struck the ground at an angle of 30° and at a distance of 30. Find the height of the whole tree

Concept: Heights and Distances
Chapter: [0.06] Trigonometry
[4]4.3

A (5, 4), B (-3, -2) and C (1, -8) are the vertices of a triangle ABC. Find the equations of the median AD and line parallel to AC passing through the point B.

Concept: General Equation of a Line
Chapter: [0.04] Co-ordinate Geometry
[10]5
[5]5.1

Prove that, in a right-angled triangle, the square of the hypotenuse is equal to the sum of the square of remaining two sides

Concept: Right-angled Triangles and Pythagoras Property
Chapter: [0.02] Pythagoras Theorem
[5]5.2

ΔSHR ~ ΔSVU. In ΔSHR, SH = 4.5 cm, HR = 5.2 cm, SR = 5.8 cm and (SH)/(SV)=3/5. Construct ΔSVU.

Concept: Division of a Line Segment
Chapter: [0.04] Co-ordinate Geometry [0.05] Geometric Constructions
[5]5.3

If ‘V’ is the volume of a cuboid of dimensions a × b × c and ‘S’ is its surface area, then prove that: 1/V = 2/S[1/a +1/b + 1/c]

Concept: Surface Area of a Combination of Solids
Chapter: [0.07] Mensuration

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