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Question Paper Solutions for Geometry A 2016-2017 SSC (Marathi Semi-English) 10th

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2016-2017 March
Marks: 40

[5]1 | Solve any five sub-equations

In the following figure, seg BE ⊥ seg AB and seg BA ⊥ seg AD. If BE = 6 and

\[AD = 9 find \frac{A\left( \Delta ABE \right)}{A\left( \Delta BAD \right)} \cdot\]


Chapter: [1] Similarity
Concept: Similarity of Triangles

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

Chapter: [3] Circle
Concept: Touching Circles

Find the height of an equilateral triangle whose side is 6 units.

Chapter: [2] Pythagoras Theorem
Concept: 30 - 60 - 90 and 45 - 45 - 90 Theorem

If the angle θ = –45° , find the value of tan θ.

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

Find the slope and y – intercept of the line y = 3x – 5.

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

Find the circumferences of a circle whose radius is 7 cm.

Chapter: [3] Circle
Concept: Tangents and Its Properties
[8]2 | Solve any four sub-questions

In the following figure, in ΔPQR, seg RS is the bisector of ∠PRQ. If PS = 6, SQ = 8, PR = 15, find QR.

Chapter: [1] Similarity
Concept: Similarity of Triangles

In the given figure PA = 10, PB = 2 and PC = 5. Find PD.

Chapter: [3] Circle
Concept: Number of Tangents from a Point to a Circle

Draw ∠ABC of measures 135°and bisect it.

Chapter: [5] Geometric Constructions
Concept: Basic Geometric Constructions

Find the sine ratio of θ in standard position whose terminal arm passes through (3, 4)

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

Find the slope of the line passing through the points G(4, 5) and H (–1, –2).

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

The dimensions of a cuboid in cm are 50 × 18 × 10. Find its volume.

Chapter: [7] Mensuration
Concept: Surface Area of a Combination of Solids
[9]3 | Solve any three sub-questions ;

Prove that: If the angles of a triangle are 45° – 45° – 90°, then each of the perpendicular sides is \[\frac{1}{\sqrt{2}}\]times the hypotenuse.”


Chapter: [6] Trigonometry
Concept: Angles in Standard Position

Find the angle between two radii at the centre of the circle as shown in the figure. Lines PA and PB are tangents to the circle at other ends of the radii and ∠APR = 140°.

Chapter: [3] Circle
Concept: Number of Tangents from a Point to a Circle

Construct tangents to the circle from the point B, having radius 3.2 cm and centre 'C'. Point B is at a distance 7.6 cm from the centre.

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

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: [6] Trigonometry
Concept: Heights and Distances

The volume of a cube is 343 cm3. Find its total surface area.

Chapter: [7] Mensuration
Concept: Surface Area of a Combination of Solids
[8]4 | Solve any two sub questions :

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

Chapter: [3] Circle
Concept: Cyclic Properties

Eliminate θ, if
x = 3 cosec θ + 4 cot θ
y = 4 cosec θ – 3 cot θ

Chapter: [6] Trigonometry
Concept: Trigonometric Identities

A toy is a combination of a cylinder, hemisphere and a cone, each with radius 10 cm as shown in the figure. Height of the conical part is 10 cm and total height is 60 cm. Find the total surface area of the toy.

(π=3.14, 2–√=1.41)

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

In the given figure, AD is the bisector of the exterior ∠A of ∆ABC. Seg AD intersects the side BC produced in D. Prove that :

\[\frac{BD}{CD} = \frac{AB}{AC}\]


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

Construct the circumcircle and incircle of an equilateral ∆XYZ with side 6.5 cm and centre O. Find the ratio of the radii of incircle and circumcircle.

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

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

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

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