In the following figure RP: PK= 3:2, then find the value of A(ΔTRP):A(ΔTPK).

Chapter: [1] Similarity

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

Chapter: [3] Circle

If the angle θ = -60° , find the value of sinθ .

Chapter: [6] Trigonometry

Find the slope of the line passing through the points A(2,3) and B(4,7).

Chapter: [4] Co-ordinate Geometry

The radius of a circle is 7 cm. find the circumference of the circle.

Chapter: [7] Mensuration

If the sides of a triangle are 6 cm, 8 cm and 10 cm, respectively, then determine whether the triangle is a right angle triangle or not.

Chapter: [2] Pythagoras Theorem

In the figure given below, Ray PT is bisector of ∠QPR. If PQ = 5.6 cm, QT = 4 cm and TR = 5 cm, find the value of x .

Chapter: [1] Similarity

In the following figure, Q is the center of the circle. PM and PN are tangents to the circle. If ∠MPN = 40° , find ∠MQN.

Chapter: [3] Circle

Write the equation 2x - 3y - 4 = 0 in the slope intercept form. Hence, write the slope and y-intercept of the line.

Chapter: [4] Co-ordinate Geometry

If `cosθ=1/sqrt(2)`, where θ is an acute angle, then find the value of sinθ.

Chapter: [6] Trigonometry

If (4,-3) is a point on the line AB and slope of the line is (-2), write the equation of the line AB.

Chapter: [4] Co-ordinate Geometry

Draw a tangent at any point ‘P’ on the circle of radius 3.5 cm and centre O.

Chapter: [5] Geometric Constructions

In a triangle ABC, line l || Side BC and line l intersects side AB and AC in points P and Q, respectively. Prove that: `"AP"/"BP"="AQ"/"QC"`

Chapter: [1] Similarity

In figure, ΔABC is an isosceles triangle with perimeter 44 cm. The base BC is of length 12 cm. Side AB and side AC are congruent. A circle touches the three sides as shown in the figure below. Find the length of the tangent segment from A to the circle.

Chapter: [7] Mensuration

Draw tangents to the circle with center ‘C’ and radius 3.6 cm, from a point B at a distance of 7.2 cm from the center of the circle.

Chapter: [5] Geometric Constructions

Prove that:

sec^{2}θ + cosec^{2}θ = sec^{2}θ x cosec^{2}θ

Chapter: [6] Trigonometry

Write the equation of each of the following lines:

- The x-axis and the y-axis.
- The line passing through the origin and the point (-3, 5).
- The line passing through the point (-3, 4) and parallel to X-axis.

Chapter: [4] Co-ordinate Geometry

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

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

Chapter: [3] Circle

The sum of length, breadth and height of a cuboid is 38 cm and the length of its diagonal is 22 cm. Find the total surface area of the cuboid.

Chapter: [7] Mensuration

In triangle ABC, ∠C=90°. Let BC= a, CA= b, AB= c and let 'p' be the length of the perpendicular from 'C' on AB, prove that:

1. cp = ab

2. `1/p^2=1/a^2+1/b^2`

Chapter: [2] Pythagoras Theorem

Construct the circumcircle and incircle of an equilateral triangle ABC with side 6 cm and centre O. Find the ratio of radii of circumcircle and incircle.

Chapter: [5] Geometric Constructions

There are three stair-steps as shown in the figure below. Each stair step has width 25 cm, height 12 cm and length 50 cm. How many bricks have been used in it, if each brick is 12.5 cm x 6.25 cm x 4 cm?

Chapter: [6] Trigonometry

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## Maharashtra State Board previous year question papers Class 10th Board Exam Geometry with solutions 2013 - 2014

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