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Question Bank Solutions for SSC (Marathi Semi-English) 10th Standard [इयत्ता १० वी] - Maharashtra State Board - Geometry

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In ∆PQR, PM = 15, PQ = 25 PR = 20, NR = 8. State whether line NM is parallel to side RQ. Give reason. 

[0.01] Similarity
Chapter: [0.01] Similarity
Concept: Property of three parallel lines and their transversals

In the given figure seg PS is the median of ∆PQR and PT ⊥ QR. Prove that,

\[{PR}^2 = {PS}^2 + QR \times ST + \left( \frac{QR}{2} \right)^2\]

\[{PQ}^2 = {PS}^2 - QR \times ST + \left( \frac{QR}{2} \right)^2\]
[0.02] Pythagoras Theorem
Chapter: [0.02] Pythagoras Theorem
Concept: Apollonius Theorem

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

[0.02] Pythagoras Theorem
Chapter: [0.02] Pythagoras Theorem
Concept: Apollonius Theorem

In the given figure, chord MN and chord RS intersect at point D.
(1) If RD = 15, DS = 4, MD = 8 find DN
(2) If RS = 18, MD = 9, DN = 8 find DS

[0.03] Circle
Chapter: [0.03] Circle
Concept: Theorem of External Division of Chords

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

Out of the following which is the Pythagorean triplet?

[0.02] Pythagoras Theorem
Chapter: [0.02] Pythagoras Theorem
Concept: Apollonius Theorem

Some question and their alternative answer are given.

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?

[0.02] Pythagoras Theorem
Chapter: [0.02] Pythagoras Theorem
Concept: Apollonius Theorem

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

 Out of the dates given below which date constitutes a Pythagorean triplet ?

[0.02] Pythagoras Theorem
Chapter: [0.02] Pythagoras Theorem
Concept: Apollonius Theorem

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

If a, b, c are sides of a triangle and a+ b= c2, name the type of triangle.

[0.02] Pythagoras Theorem
Chapter: [0.02] Pythagoras Theorem
Concept: Apollonius Theorem

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

Find perimeter of a square if its diagonal is \[10\sqrt{2}\]

[0.02] Pythagoras Theorem
Chapter: [0.02] Pythagoras Theorem
Concept: Apollonius Theorem

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.

[0.02] Pythagoras Theorem
Chapter: [0.02] Pythagoras Theorem
Concept: Apollonius Theorem

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

Height and base of a right angled triangle are 24 cm and 18 cm find the length of its hypotenuse

[0.02] Pythagoras Theorem
Chapter: [0.02] Pythagoras Theorem
Concept: Apollonius Theorem

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

 In ∆ABC, AB = \[6\sqrt{3}\] cm, AC = 12 cm, BC = 6 cm. Find measure of ∠A.

[0.02] Pythagoras Theorem
Chapter: [0.02] Pythagoras Theorem
Concept: Apollonius Theorem

Solve the following example.

 Find the height of an equilateral triangle having side 2a.

[0.02] Pythagoras Theorem
Chapter: [0.02] Pythagoras Theorem
Concept: Apollonius Theorem

Do sides 7 cm, 24 cm, 25 cm form a right angled triangle ? Give reason

[0.02] Pythagoras Theorem
Chapter: [0.02] Pythagoras Theorem
Concept: Apollonius Theorem

Find the length a diagonal of a rectangle having sides 11 cm and 60 cm.

[0.02] Pythagoras Theorem
Chapter: [0.02] Pythagoras Theorem
Concept: Apollonius Theorem

Find the length of the hypotenuse of a right angled triangle if remaining sides are 9 cm and 12 cm.

[0.02] Pythagoras Theorem
Chapter: [0.02] Pythagoras Theorem
Concept: Apollonius Theorem

Find the centroid of the triangle whose vertice is given below.

(–7, 6), (2, –2), (8, 5)

[0.04] Co-ordinate Geometry
Chapter: [0.04] Co-ordinate Geometry
Concept: Centroid Formula

Find the centroid of the triangle whose vertice is given below.

 (3, –5), (4, 3), (11, –4)

[0.04] Co-ordinate Geometry
Chapter: [0.04] Co-ordinate Geometry
Concept: Centroid Formula

Find the centroid of the triangle whose vertice is given below.

(4, 7), (8, 4), (7, 11)

[0.04] Co-ordinate Geometry
Chapter: [0.04] Co-ordinate Geometry
Concept: Centroid Formula

In ∆ABC, G (–4, –7) is the centroid. If A (–14, –19) and B(3, 5) then find the co–ordinates of C.

[0.04] Co-ordinate Geometry
Chapter: [0.04] Co-ordinate Geometry
Concept: Centroid Formula
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Question Bank Solutions for SSC (Marathi Semi-English) 10th Standard [इयत्ता १० वी] Maharashtra State Board Geometry. You can further filter Question Bank Solutions by subjects and topics. Solutions for most of the questions for Maharashtra State Board can be found here on Shaalaa.com. You can use these solutions to prepare for your studies and ace in exams. Solving questions is a great way to practice and with Shaalaa.com, you can answer a question and then also check your answer with the solutions provided.
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