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# Important Questions for SSC (English Medium) Class 10th Board Exam - Maharashtra State Board - Geometry

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In the following figure, in ΔPQR, seg RS is the bisector of ∠PRQ. If PS = 6, SQ = 8, PR = 15, find QR. Appears in 3 question papers
Chapter:  Similarity
Concept: Similarity of Triangles

In the following figure RP: PK= 3:2, then find the value of A(ΔTRP):A(ΔTPK). Appears in 3 question papers
Chapter:  Similarity
Concept: Properties of Ratios of Areas of Two Triangles

Prove that ‘the opposite angles of a cyclic quadrilateral are supplementary’.

Appears in 3 question papers
Chapter:  Circle

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

Appears in 3 question papers
Chapter:  Circle
Concept: Touching Circles

A person standing on the bank of river observes that the angle of elevation of the top of a tree standing on the opposite bank is 60°. When he moves 40 m away from the bank, he finds the angle of elevation to be 30°. Find the height of the tree and width of the river. (sqrt 3=1.73)

Appears in 3 question papers
Chapter:  Trigonometry
Concept: Heights and Distances

Using Euler’s formula, find V if E = 30, F = 12.

Appears in 3 question papers
Chapter:  Mensuration
Concept: Euler's Formula

In Fig. 3, AP and BP are tangents to a circle with centre O, such that AP = 5 cm and ∠APB = 60°. Find the length of chord AB. Appears in 3 question papers
Chapter:  Mensuration
Concept: Areas of Sector and Segment of a Circle

A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank which is 10 m in diameter and 2 m deep. If the water flows through the pipe at the rate of 4 km per hour, in how much time will the tank be filled completely?

Appears in 3 question papers
Chapter:  Mensuration
Concept: Surface Area of a Combination of Solids

In the following figure seg AB ⊥ seg BC, seg DC ⊥ seg BC. If AB = 2 and DC = 3, find (A(triangleABC))/(A(triangleDCB)) Appears in 2 question papers
Chapter:  Similarity
Concept: Properties of Ratios of Areas of Two Triangles

Prove that the angle bisector of a triangle divides the side opposite to the angle in the ratio of the remaining sides.

Appears in 2 question papers
Chapter:  Similarity
Concept: Similarity of Triangles

In the following figure, seg BE ⊥ seg AB and seg BA ⊥ seg AD. If BE = 6 and $\text{AD} = 9 \text{ find} \frac{A\left( \Delta ABE \right)}{A\left( \Delta BAD \right)} \cdot$ Appears in 2 question papers
Chapter:  Similarity
Concept: Similarity of Triangles

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 :

$\frac{BD}{CD} = \frac{AB}{AC}$ Appears in 2 question papers
Chapter:  Similarity
Concept: Properties of Ratios of Areas of Two Triangles

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

Appears in 2 question papers
Chapter:  Pythagoras Theorem
Concept: 30 - 60 - 90 and 45 - 45 - 90 Theorem

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

In a right angled triangle, if sum of the squares of the sides making right angle is 169 then what is the length of the hypotenuse?

Appears in 2 question papers
Chapter:  Pythagoras Theorem
Concept: Apollonius Theorem

Prove that “The lengths of the two tangent segments to a circle drawn from an external point are equal.”

Appears in 2 question papers
Chapter:  Circle
Concept: Number of Tangents from a Point on a Circle

If two circles with radii 5 cm and 3 cm respectively touch internally, find the distance between their centres.

Appears in 2 question papers
Chapter:  Circle
Concept: Touching Circles

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

Appears in 2 question papers
Chapter:  Circle
Concept: Touching Circles

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

Appears in 2 question papers
Chapter:  Circle
Concept: Tangents and Its Properties

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

Appears in 2 question papers
Chapter:  Circle
Concept: Cyclic Properties

Choose the correct alternative.

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

Appears in 2 question papers
Chapter:  Circle
Concept: Inscribed Angle
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Important Questions for SSC (English Medium) Class 10th Board Exam Maharashtra State Board Geometry. You can further filter Important Questions by subjects and topics. Chapter wise important Questions for Class 10th Board Exam Maharashtra State Board. it gets easy to find all Class 10th Board Exam important questions with answers in a single place for students. Saving time and can then focus on their studies and practice. Important questions for Class 10th Board Exam chapter wise with solutions

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