SSC (English Medium) १० वीं कक्षा - Maharashtra State Board Question Bank Solutions for Geometry Mathematics 2

A circle is inscribed in square ABCD of side 14 cm. Complete the following activity to find the area of the shaded portion.
  Activity:

Area of square ABCD = ______

= 14²  
 = 196 cm² 
Area of circle = πr²     = `22/7xx 7^2`   
= ____ cm²

Area of shaded portion = Area of square ABCD – Area of circle   

 = 196 – _______

= _____ cm²

If cosθ = `5/13`, then find sinθ. 

Verify that the points A(–2, 2), B(2, 2) and C(2, 7) are the vertices of a right-angled triangle. 

Find the length of diagonal of the square whose side is 8 cm.

Find the side of the square whose diagonal is `16sqrt(2)` cm.

If sec θ = `25/7`, find the value of tan θ.

Solution:

1 + tan² θ = sec² θ

∴ 1 + tan² θ = `(25/7)^square`

∴ tan² θ = `625/49 - square`

= `(625 - 49)/49`

= `square/49`

∴ tan θ = `square/7` ........(by taking square roots)

In the given figure `square`ABCD is a square of side 50 m. Points P, Q, R, S are midpoints of side AB, side BC, side CD, side AD respectively. Find area of shaded region

If sin θ + sin² θ = 1 show that: cos² θ + cos⁴ θ = 1

Choose the correct alternative:

If length of sides of a triangle are a, b, c and a² + b² = c², then which type of triangle it is?

From the given figure, in ∆ABQ, if AQ = 8 cm, then AB =?

In a right angled triangle, if length of hypotenuse is 25 cm and height is 7 cm, then what is the length of its base?

From given figure, In ∆ABC, If AC = 12 cm. then AB =?

Activity: From given figure, In ∆ABC, ∠ABC = 90°, ∠ACB = 30°

∴ ∠BAC = `square`

∴ ∆ABC is 30° – 60° – 90° triangle

∴ In ∆ABC by property of 30° – 60° – 90° triangle.

∴ AB = `1/2` AC and `square` = `sqrt(3)/2` AC

∴ `square` = `1/2 xx 12` and BC = `sqrt(3)/2 xx 12`

∴ `square` = 6 and BC = `6sqrt(3)`

Prove the following theorem:

Angles inscribed in the same arc are congruent.

Choose the correct alternative:

cos θ. sec θ = ?

Choose the correct alternative:

sec 60° = ?

Choose the correct alternative:

1 + cot²θ = ? 

Choose the correct alternative:

cot θ . tan θ = ?

Choose the correct alternative:

sec²θ – tan²θ =?

sin²θ + sin²(90 – θ) = ?

Choose the correct alternative:

`(1 + cot^2"A")/(1 + tan^2"A")` = ?