Plane Geometry problems
- 1. PQRS is a square. The ? SRP is equal to :
Options- A. 45°
- B. 90°
- C. 100°
- D. 60° Discuss
Correct Answer: 45°
Explanation:
- 2. The two sides of a right triangle containing the right angle measure 3 cm and 4 cm. The radius of the in circle of the triangle is :
Options- A. 3.5 cm
- B. 1.75 cm
- C. 1 cm
- D. 0.875 cm Discuss
Correct Answer: 1 cm
Explanation:
- 3. If one of the diagonals of a rhombus is equal to its side, then the diagonals of the rhombus are in the ratio :
Options- A. ?3 : 1
- B. ?2 : 1
- C. 3 : 1
- D. 2 : 1 Discuss
Correct Answer: ?2 : 1
Explanation:
Let ABCD is a rhombus in which AB = BC = CD = DA = diagonal CA.
In triangle ABC ,
AB = BC = CA , therefore ?B = 60°
?D = ?B = 60°
?A=180 - ?B = 180° - 60° =120°
?C = ?A=120°
Hence ,The ratio of diagonals = ?2 : 1
- 4. We have an angle of 2 1°/ 2 .How big it will look through a glass that magnifies things three times?
Options- A. 2 1° × 4 2
- B. 2 1° × 3 2
- C. 2 1° × 2 2
- D. 2 1° × 5 2 Discuss
Correct Answer: 2 1° × 5 2
Explanation:
- 5. Two circles of unit radius touch each other and each of them touches internally a circle of radius two, as shown in the following figure. The radius of the circle which thouches all the three circles:
Options- A. 5
- B. 3 2
- C. 2 3
- D. 2 5 Discuss
Correct Answer: 2 3
Explanation:
- 6. If, in the following figure, PA = 8 cm, PD = 4 cm, CD equal to 3 cm, then AB is :
Options- A. 3.0 cm
- B. 3.5 cm
- C. 4.0 cm
- D. 4.5 cm Discuss
Correct Answer: 4.5 cm
Explanation:
- 7. In the given figure, what is the length of AD in terms of b and c :
Options- A. bc b2+c2
- B. b2+c2 bc
- C. ? b2+c2 bc
- D. bc ? b2+c2 Discuss
Correct Answer: bc ? b2+c2
Explanation:
- 8. In a quadrilateral ABCD, ?B = 90° and AD 2 = AB 2 + BC 2 + CD 2, then ?ACD is equal to:
Options- A. 90°
- B. 60°
- C. 30°
- D. 20° Discuss
Correct Answer: 90°
Explanation:
In a quadrilateral ABCD,
Given :- ?B = 90°
AB2 + BC2 + CD2 = AC2 + CD2 = AD2 { ? In triangle ABC , AB2 + BC2 = AC2 }
So, in triangle ACD, angle opposite to AD = 90° ( by Converse of Pythagoras theorem)
? ?ACD = 90°
- 9. If P and Q are the mid points of the sides CA and GB respectively of a triangle ABC, right-angled at C. Then the value of 4 ( AQ 2 + BP 2) is equal to :
Options- A. 4 BC2
- B. 5 AB2
- C. 2 AC2
- D. 2 BC2 Discuss
Correct Answer: 5 AB2
Explanation:
- 10. In a triangle ABC, ?A = x°, ?B = y° and ?C = (y + 20)°. If 4x ? y = 10, then the triangle is :
Options- A. Right-angle
- B. Obtuse-angled
- C. Equilateral
- D. None of these Discuss
Correct Answer: Right-angle
Explanation:
Given :- ?A = x° , ?B = y° , ?C = ( y + 20 )° and 4x ? y = 10
We know that , ?A + ?B + ?C = 180°
? x + y + ( y + 20 ) = 180°
? x + 2y = 180 - 20 = 160° ........... ( ? )
4x ? y = 10 ........... ( ? )
From ( ? ) and ( ? ) , we get
? y = 70 , x = 20
? The angles of the triangle are 20° , 70° , 90° .
Hence , the triangle will be Right-angle triangle .
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