Ponit M is the mid point of seg AB and AB = 14 then AM = ?

Concept: Basic Geometric Constructions

Observe the adjoining figure and write down one pair of interior angles.

Concept: Basic Geometric Constructions

If Δ ABC ∼ Δ XYZ then complete the following brackets.

`(AB)/(XY) = /(YZ) = (AC)/`

Concept: Basic Geometric Constructions

Draw ∠ ARP= 115° and bisect it.

Concept: Basic Geometric Constructions

From the figure find the value of sinθ.

Concept: Basic Geometric Constructions

Write down the equation of X- axis.

Concept: Basic Geometric Constructions

Radius of a sphere is 14 cm. Find the surface area of the sphere.

Concept: Introduction of Surface Areas and Volumes

P is the centre of the circle and its radius is

10 cm. Distance of a chord AB from the centre is 6 cm. Find the length of chord AB.

Concept: Theorem - Converse of Tangent at Any Point to the Circle is Perpendicular to the Radius

LMNP is a parallelogram. From the information given in the figure fill in the following boxes.

MN = cm

PN = cm

∠ M =

∠ N =

Concept: Centroid Formula

Select the correct alternative answer and write it.

The ratio of corresponding sides of similar triangles is 5 : 7, then what is

the ratio of their areas ?

(A)25 : 49 (B) 49 : 25 (C) 5 : 7 (D) 7 : 5

Concept: Similar Triangles

Select the correct alternative answer and write it.

What is the total surface area of a solid hemisphere whose radius is r ?

(A) 4pr^{2 } (B) pr2 (C) 2pr^{2 } (D) 3pr^{2}

Concept: Surface Area of a Combination of Solids

Find the length of the hypotenuse in a right angled triangle where the sum

of the squares of the sides making right angle is 169.

(A)15 (B) 13 (C) 5 (D) 12

Concept: Similarity in Right Angled Triangles

How many common tangents can be drawn to two circles, touching each

other externally?

One

Two

Three

Four

Concept: Tangent to a Circle

In the given figure, CB ⊥ AB, DA ⊥ AB.

if BC = 4, AD = 8 then `(A(Δ ABC))/(A(Δ ADB))` find.

Concept: Similar Triangles

Find the length of the hypotenuse of a square whose side is 16 cm.

Concept: Section Formula

Radius of a sector of a circle is 21 cm. If length of arc of that sector is

55 cm, find the area of the sector.

Concept: Tangent Properties - If Two Circles Touch, the Point of Contact Lies on the Straight Line Joining Their Centers

In the figure m(arc LN) = 110o,

m(arc PQ) = 50o then complete the following activity to find ∠ LMN.

∠ LMN = 12 [m(arc LN) - ]

∴ ∠ LMN = 12 [ - 50o]

∴ ∠ LMN = 12 ×

∴ ∠ LMN =

Concept: Cyclic Properties

Complete the following activity to draw a tangent to a circle at a point on

the circle.

Draw a circle of radius 2.2 cm with O as centre.

↓

Take any point P on the circle and draw ray OP.

↓

Draw a perpendicular line to the ray at point P.

↓

Name the perpendilcular line as l

l is the tangent at point P.

Concept: Construction of Tangents to a Circle

A tank of cylindrical shape has radius 2.8 m and its height 3.5 m. Complete

the activity to find how many litres of water the tank will contain.

Capacity of water tank = Volume of cylindrical tank

Concept: Introduction of Surface Areas and Volumes

In Δ DEF, line PQ || side EF, If DP = 2.4,

PE = 7.2, PQ = 1 then find QF.

Concept: General Equation of a Line

In the figure Q is the contact point. If

PQ = 12, PR = 8, then PS = ?

Concept: Cyclic Properties

If `secθ = 25/7 ` then find tanθ.

Concept: Trigonometric Identities

Prove that, in a right angled triangle, the square of the hypotenuse is

equal to the sum of the squares of remaining two sides.

Concept: Similarity in Right Angled Triangles

Show that A(-4, -7), B(-1, 2), C(8, 5) and D(5, -4) are the vertices of a

rhombus ABCD.

Concept: Concepts of Coordinate Geometry

A storm broke a tree and the tree top rested on ground 20 m away from the

base of the tree, making an angle of 60o with the ground. Find the height

of the tree.

Concept: Heights and Distances

Draw a circle with centre P and radius 2.1 cm. Take point Q at a distance

5.2 cm from the centre. Draw tangents to the circle from point Q. Measure

and write the length of a tangent segment.

Concept: Construction of Tangents to a Circle

AB and AC are the two chords of a circle whose radius is r. If p and q are

the distance of chord AB and CD, from the centre respectively and if

AB = 2AC then proove that 4q2 = p^{2} + 3r^{2}.

Concept: Distance Formula

Δ SHR ∼ Δ SVU. In Δ SHR, SH = 4.5 cm, HR = 5.2 cm, SR = 5.8 cm and

SHSV = 53 then draw Δ SVU.

Concept: Division of a Line Segment

Radius of circular base of an ear of corn is 6.6 cm and its length is

11.2 cm. If on an average 1 sqcm area contains 2 corn kernels, find the

total number of kernels on a corn.

Concept: Theorem - Converse of Tangent at Any Point to the Circle is Perpendicular to the Radius

In Δ ABC and Δ PQR,

∠ ABC ≅ ∠ PQR, seg BD and

seg QS are angle bisector.

`If (l(AD))/(l(PS)) = (l(DC))/(l(SR))`

Prove that : Δ ABC ∼ Δ PQR

Concept: Property of an Angle Bisector of a Triangle

## Maharashtra State Board previous year question papers 10th Geometry with solutions 2018 - 2019

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