SSC (English Medium) इयत्ता १० वी - Maharashtra State Board Question Bank Solutions

In the following figure, O is the centre of the circle. ∠ABC is inscribed in arc ABC and  ∠ ABC = 65°. Complete the following activity to find the measure of ∠AOC. 

∠ABC = `1/2`m ______  (Inscribed angle theorem) 
______ × 2 = m(arc AXC)  
m(arc AXC) = _______
∠AOC = m(arc AXC)  (Definition of measure of an arc)  
∠AOC = ______

Find the side and perimeter of a square whose diagonal is `13sqrt2` cm. 

From given figure, In ∆ABC, AB ⊥ BC, AB = BC then m∠A = ?

From given figure, In ∆ABC, AB ⊥ BC, AB = BC, AC = `2sqrt(2)` then l (AB) = ?

From given figure, In ∆ABC, AB ⊥ BC, AB = BC, AC = `5sqrt(2)` , then what is the height of ∆ABC?

Find the height of an equilateral triangle having side 4 cm?

In the figure, PQRS is a square with side 10 cm. The sectors drawn with P and R as centres form the shaded figure. Find the area of the shaded figure. (Use π = 3.14)

In a ΔABC, ∠CAB is an obtuse angle. P is the circumcentre of ∆ABC. Prove that ∠CAB – ∠PBC = 90°.

In the above figure, ∠ABC is inscribed in arc ABC.

If ∠ABC = 60°. find m ∠AOC.

Solution:

∠ABC = `1/2` m(arc AXC)   ......`square`

60° = `1/2` m(arc AXC) 

`square` = m(arc AXC) 

But m ∠AOC = \[\boxed{m(arc ....)}\]   ......(Property of central angle)

∴ m ∠AOC = `square`

Adjacent sides of a parallelogram are 11 cm and 17 cm. If the length of one of its diagonal is 26 cm, find the length of the other.

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

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.

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

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

PR² = PS² + QR × ST + `("QR"/2)^2`

In ∆ABC, point M is the midpoint of side BC. If, AB² + AC² = 290 cm², AM = 8 cm, find BC.

Out of the following, which is the Pythagorean triplet?

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?

Find the perimeter of a square if its diagonal is `10sqrt2` cm:

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.