# 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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