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

Concept: Similarity of Triangles

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

Concept: Touching Circles

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

Concept: 30 - 60 - 90 and 45 - 45 - 90 Theorem

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

Concept: Trigonometric Ratios of Complementary Angles

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

Concept: Intercepts Made by a Line

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

Concept: Tangents and Its Properties

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

Concept: Similarity of Triangles

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

Concept: Number of Tangents from a Point to a Circle

Draw ∠ABC of measures 135^{°}and bisect it.

Concept: Basic Geometric Constructions

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

Concept: Trigonometric Ratios of Complementary Angles

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

Concept: Slope of a Line

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

Concept: Surface Area of a Combination of Solids

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.”

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°.

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.

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)

Concept: Heights and Distances

The volume of a cube is 343 cm^{3}. Find its total surface area.

Concept: Surface Area of a Combination of Solids

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

Concept: Cyclic Properties

Eliminate θ, if

x = 3 cosec θ + 4 cot θ

y = 4 cosec θ – 3 cot θ

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)

Concept: Surface Area of a Combination of Solids

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 :

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.

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.

Concept: General Equation of a Line

## Maharashtra State Board previous year question papers Class 10th Board Exam Geometry with solutions 2016 - 2017

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