# Geometry Shaalaa.com Model Set 4 2019-2020 SSC (Marathi Semi-English) Class 10th Board Exam Question Paper Solution

Geometry [Shaalaa.com Model Set 4]
Date: March 2020
Duration: 2h

[8]1
[4]1.A | MCQs
[1]1.A.i

In the given figure, seg XY || seg BC, then which of the following statements is true?

$\frac{AB}{AC} = \frac{AX}{AY}$

$\frac{AX}{XB} = \frac{AY}{AC}$

$\frac{AX}{YC} = \frac{AY}{XB}$

$\frac{AB}{YC} = \frac{AC}{XB}$

Concept: Similarity of Triangles
Chapter: [1] Similarity
[1]1.A.ii

Select the correct alternative for the following question.

(3) If ∆ABC ~ ∆PQR and (AB)/(PQ) = 7/5, then ...............

∆ABC is bigger.

∆PQR is bigger.

Both triangles will be equal.

Can not be decided.

Concept: Construction of Tangent to the Circle from the Point on the Circle
Chapter: [5] Geometric Constructions
[1]1.A.iii

Some question and their alternative answer are given. Select the correct alternative.

Altitude on the hypotenuse of a right angled triangle divides it in two parts of lengths 4 cm and 9 cm. Find the length of the altitude.

9 cm

4 cm

6 cm

$2\sqrt{6}$ cm

Concept: Apollonius Theorem
Chapter: [2] Pythagoras Theorem
[1]1.A.iv

Choose the correct alternative.

∠ACB is inscribed in arc ACB of a circle with centre O. If ∠ACB = 65°, find m(arc ACB).

65°

130°

295°

230°

Concept: Inscribed Angle
Chapter: [3] Circle
[4]1.B
[1]1.B.i

In the given figure, BC ⊥ AB, AD ⊥ AB, BC = 4, AD = 8, then find $\frac{A\left( ∆ ABC \right)}{A\left( ∆ ADB \right)} .$

Concept: Similar Triangles
Chapter: [1] Similarity
[1]1.B.ii

∆AMT ~ ∆AHE. In ∆AMT, AM = 6.3 cm, ∠TAM = 50°, AT = 5.6 cm.  $\frac{AM}{AH} = \frac{7}{5} .$Construct ∆AHE.

Concept: Division of a Line Segment
Chapter: [4] Co-ordinate Geometry [5] Geometric Constructions
[1]1.B.iii

Determine whether the following point is collinear.

D(–2, –3), E(1, 0), F(2, 1)

Concept: Slope of a Line
Chapter: [4] Co-ordinate Geometry
[1]1.B.iv

Find the surface area and the volume of a beach ball shown in the figure

Concept: Surface Area of a Combination of Solids
Chapter: [7] Mensuration
[12]2
[4]2.A | Solve any 2 of the following
[2]2.A.i

Are the triangles in the given figure similar? If yes, by which test ?

Concept: Similarity of Triangles
Chapter: [1] Similarity
[2]2.A.ii

In ∆ABC, point M is the midpoint of side BC.
If, AB+ AC= 290 cm2, AM = 8 cm, find BC.

Concept: Apollonius Theorem
Chapter: [2] Pythagoras Theorem
[2]2.A.iii

In the given figure, O is the centre of the ci
rcle. Seg AB, seg AC are tangent segments. Radius of the circle is r and l(AB) = r , Prove that, ▢ABOC is a square.

Concept: Tangent Segment Theorem
Chapter: [3] Circle
[8]2.B | Solve any 4 of the following
[2]2.B.i

∆ABC ~ ∆LBN. In ∆ABC, AB = 5.1cm, ∠B = 40°, BC = 4.8 cm,$\frac{AC}{LN} = \frac{4}{7}$. Construct ∆ABC and ∆LBN.

Concept: Division of a Line Segment
Chapter: [4] Co-ordinate Geometry [5] Geometric Constructions
[2]2.B.ii

From the top of the light house, an observer looks at a ship and finds the angle of depression to be 30°. If the height of the light-house is 100 meters, then find how far the ship is from the light-house.

Concept: Heights and Distances
Chapter: [6] Trigonometry
[2]2.B.iii

If $\sin\theta = \frac{7}{25}$, find the values of cosθ and tan​θ.

Concept: Application of Trigonometry
Chapter: [6] Trigonometry
[2]2.B.iv

In the given figure, O is the centre of the circle and B is a point of contact. seg OE ⊥ seg AD, AB = 12, AC = 8, find
(1) AD (2) DC (3) DE.

Concept: Tangent Segment Theorem
Chapter: [3] Circle
[2]2.B.v

In the given figure, a cylindrical wrapper of flat tablets is shown. The radius of a tablet is 7 mm and its thickness is 5 mm. How many such tablets are wrapped in the wrapper?

Concept: Surface Area of a Combination of Solids
Chapter: [7] Mensuration
[9]3
[3]3.A | Solve any 1 of the following
[3]3.A.i

If ∆ABC ~ ∆PQR, A (∆ABC) = 80, A (∆PQR) = 125, then fill in the blanks. $\frac{A\left( ∆ ABC \right)}{A\left( ∆ . . . . \right)} = \frac{80}{125} \therefore \frac{AB}{PQ} = \frac{......}{......}$

Concept: Areas of Two Similar Triangles
Chapter: [1] Similarity
[3]3.A.ii

In the given figure, M is the centre of the circle and seg KL is a tangent segment.
If MK = 12, KL = $6\sqrt{3}$ then find –
(2) Measures of ∠K and ∠M.

Concept: Tangent Segment Theorem
Chapter: [3] Circle
[6]3.B | Solve any 2 of the following
[3]3.B.i

In the given figure, the vertices of square DEFG are on the sides of ∆ABC. ∠A = 90°. Then prove that DE2 = BD × EC (Hint: Show that ∆GBD is similar to ∆CFE. Use GD = FE = DE.)

Concept: Property of three parallel lines and their transversals
Chapter: [1] Similarity
[3]3.B.ii

Draw a circle with centre P. Draw an arc AB of 100° measure. Draw tangents to the circle at point A and point B.

Concept: Construction of Tangents to a Circle
Chapter: [5] Geometric Constructions
[3]3.B.iii

Find the coordinates of circumcentre and radius of circumcircle of ∆ABC if A(7, 1), B(3, 5) and C(2, 0) are given.

Concept: Concepts of Coordinate Geometry
Chapter: [4] Co-ordinate Geometry
[3]3.B.iv

The line segment AB is divided into five congruent parts at P, Q, R and S such that A–P–Q–R–S–B. If point Q(12, 14) and S(4, 18) are given find the coordinates of A, P, R, B.

Concept: Division of a Line Segment
Chapter: [4] Co-ordinate Geometry [5] Geometric Constructions
[8]4 | Solve any 2 of the following
[4]4.A

In a trapezium ABCD, seg AB || seg DC seg BD ⊥ seg AD, seg AC ⊥ seg BC, If AD = 15, BC = 15 and AB = 25. Find A(▢ABCD)

Concept: Pythagoras Theorem
Chapter: [2] Pythagoras Theorem
[4]4.B

In the given figure, a ∆ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC are of lengths 8 cm and 6 cm respectively. Find the lengths of sides AB and AC, when area of ∆ABC is 84 cm2

Concept: Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior.
Chapter: [3] Circle
[4]4.C

The difference between outer and inner curved surface areas of a hollow right circular cylinder 14cm long is 88cm2. If the volume of metal used in making cylinder is 176cm3.find the outer and inner diameters of the cylinder____?

Concept: Volume of a Combination of Solids
Chapter: [7] Mensuration
[3]5 | Solve any 1 of the following
[3]5.A

Prove that:

$\frac{\tan\theta}{\sec\theta - 1} = \frac{\tan\theta + \sec\theta + 1}{\tan\theta + \sec\theta - 1}$
Concept: Application of Trigonometry
Chapter: [6] Trigonometry
[3]5.B

In the given figure, square ABCD is inscribed in the sector A - PCQ. The radius of sector C - BXD is 20 cm. Complete the following activity to find the area of shaded region

Concept: Surface Area of a Combination of Solids
Chapter: [7] Mensuration

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