# Geometry 2015-2016 SSC (Marathi Semi-English) 10th Standard [इयत्ता १० वी] Question Paper Solution

Geometry
Date: July 2016

1 | Solve any five sub-questions:
1.i

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: [0.01] Similarity
1.ii

If two circles with diameters 8 cm and 6 cm respectively touch externally, find the distance between their centers.

Concept: Touching Circles
Chapter: [0.03] Circle
1.iii

Find the Slope of the line having inclination 45°.

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

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

Concept: Euler's Formula
Chapter: [0.07] Mensuration
1.v

Find the length of diagonal of the square whose side is 8 cm.

Concept: Right-angled Triangles and Pythagoras Property
Chapter: [0.02] Pythagoras Theorem
1.vi

For the angle in standard position if the initial arm rotates 305° in an anticlockwise direction, then state the quadrant in which the terminal arm lies.

Concept: Angles in Standard Position
Chapter: [0.06] Trigonometry
2 | Solve any four sub-questions:
2.i

Draw seg AB of length 9.7 cm. Take a point P on it such that A-P-B, AP = 3.5 cm. Construct a line MNsag AB through point P.

Concept: Division of a Line Segment
Chapter: [0.04] Co-ordinate Geometry [0.05] Geometric Constructions
2.ii

Find the trigonometric sine ratio of an angle in a standard position whose terminal arm passes through the point (3, 4).

Concept: Trigonometric Ratios in Terms of Coordinates of Point
Chapter: [0.06] Trigonometry
2.iii

In the following figure, state whether the triangles are similar. Give reason. Concept: Similar Triangles
Chapter: [0.01] Similarity
2.iv

In the following figure, seg AB is a diameter of the circle, m (arc AKC) = 40°. Find the value of m (arc BMC). Concept: Tangent to a Circle
Chapter: [0.03] Circle
2.v

Write the equation of a line passing through the point P (0,6) and having slope 6/7.

Concept: Slope of a Line
Chapter: [0.04] Co-ordinate Geometry
2.vi

Find the area of sector whose central angle and radius are 60o and 21 cm respectively.
(pi = 22/7)

Concept: Tangent to a Circle
Chapter: [0.03] Circle
3 | Solve any three sub-questions:
3.i

In the following figure, seg AB is the diameter of the circle with center P. Line CB be the tangent and line AC intersects a circle in point D. Prove that: Concept: Tangent to a Circle
Chapter: [0.03] Circle
3.ii

In the following figure, ray PT is the bisector of QPR Find the value of x and perimeter of QPR. Concept: Property of an Angle Bisector of a Triangle
Chapter: [0.01] Similarity
3.iii

The length, breadth, and height of a cuboid are in the ratio 5:4: 2. If the total surface area is 1216 cm2, find dimensions of the solid.

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

Construct the incircle of Δ RST in which RS = 6cm, ST 7 cm, RT
= 6.5 cm.

Concept: Inscribed Angle
Chapter: [0.03] Circle
3.v

Show that:

sqrt((1-cos"A")/(1+cos"A"))=cos"ecA - cotA"

Concept: Application of Trigonometry
Chapter: [0.06] Trigonometry
4 | Solve any two sub-questions:
4.i

Prove that ‘the opposite angles of a cyclic quadrilateral are supplementary’.

Chapter: [0.03] Circle
4.ii

A person standing on the bank of river observes that the angle of elevation of the top of a tree standing on the opposite bank is 60°. When he moves 40 m away from the bank, he finds the angle of elevation to be 30°. Find the height of the tree and width of the river. (sqrt 3=1.73)

Concept: Heights and Distances
Chapter: [0.06] Trigonometry
4.iii

A roller of diameter 0.9 m and the length 1.8 m is used to press the ground. Find the area of the ground pressed by it in 500 revolutions.
(pi=3.14)

Concept: Properties of Ratios of Areas of Two Triangles
Chapter: [0.01] Similarity
5 | Solve any two sub-questions:
5.i

Prove that, if a line parallel to a side of a triangle intersects the other sides in two district points, then the line divides those sides in proportion.

Concept: Property of three parallel lines and their transversals
Chapter: [0.01] Similarity
5.ii

Show that ABCD is a parallelogram if A = (4, 8), B = (5, 5), C = (2, 4), D = (1, 7)

Concept: Converse: If a pair of opposite angles of a quadrilateral is supplementary, then the quadrilateral is cyclic.
Chapter: [0.03] Circle
5.iii

ΔAMT∼ΔAHE, construct Δ AMT such that MA = 6.3 cm, ∠MAT=120°, AT = 4.9 cm and "MA"/"HA"=7/5, then construct ΔAHE.

Concept: Application of Trigonometry
Chapter: [0.06] Trigonometry

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