Discussion
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- Question
- If the sides of a right triangle are x, x + 1 and x ? 1, then the hypotenuse :
Options- A. 5
- B. 4
- C. 1
- D. 0
- Correct Answer
- 5
ExplanationFrom given figure , we have
Let, (x + 1) be the hypotenuse and perpendicular = x - 1 , base = x.
By pythagoras theorem ,
? (x + 1)2 = x2 + (x + 1)2 ? x = 4
? Hypotenuse = 4 + 1 = 5 - 1. If two diameters of a circle intersect each other at right angles, then the quadrilateral formed by joining here end points is a :
Options- A. Rhombus
- B. Rectangle
- C. Square
- D. Parallelogram Discuss
- 2. In the given figure, the side BC of a ? ABC is produced on both sides. Then ? 1 + ? 2 is equal to :
Options- A. ?A + 180°
- B. 180° ? ?A
- C. 1 (?A + 180°) 2
- D. ?A + 90° Discuss
- 3. In the given figure, which of the following is true :
Options- A. x = ? + ? + ?
- B. x + ? = ? + ?
- C. x + ? = ? + ?
- D. x + ? = ? + ? Discuss
- 4. In center of a triangle lies in the interior of :
Options- A. an isosceles triangle only
- B. any triangle
- C. an equilateral triangle only
- D. a right triangle only Discuss
- 5. In the given figure DE||BC and AD : DB = 5 : 4,
Then ar(?DFE) ar(?CFB)
Options- A. 25 81
- B. 25 16
- C. 16 25
- D. 16 81 Discuss
- 6. ABCD is a square, F is mid point of AB and E is a point on BC such that BE is one-third of BC. If area of ?FBE = 108 m 2, then the length of AC is:
Options- A. 63 m
- B. 36?2 m
- C. 63?2 m
- D. 72?2 m Discuss
- 7. ABCD is a parallelogram P, Q, R and S are points on sides AB, BC, CD and DA respectively such that AP = DR. If the area of the parallelogram ABCD is 16 cm 2, then the area of the quadrilateral PQRS is:
Options- A. 6 cm2
- B. 6.4 cm2
- C. 4 cm2
- D. 8 cm2 Discuss
- 8. The circumcentre of a triangle is always the point of intersection of the :
Options- A. Medians
- B. Bisectors
- C. Perpendiculars
- D. Perpendiculars dropped from the, vertices on the opposite side of the triangle Discuss
- 9. In the following figure, If BC = 8 cm, AB = 6 cm, AC 9 cm, then DC is equal to :
Options- A. 7 cm
- B. 4.8 cm
- C. 7.2 cm
- D. 4.5 cm Discuss
- 10. In the accompanying figure, AB is one of the diameters of the circle and OC is perpendicular to it through the centre O. If AC is 7?2 cm, then what is the area of the circle in cm 2?
Options- A. 24.5
- B. 49
- C. 98
- D. 154 Discuss
Plane Geometry problems
Search Results
Correct Answer: Square
Explanation:
From given figure , we have
In quadrilateral ABCD , we can see that
Diagonal AB = Diagonal CD ......... ( ? )
AO = OB ......... ( ? )
DO = CO ......... ( ? )
?DOB = 90° ......... ( ? )
From ( ? ) , ( ? ) , ( ? ) and ( ? ) , we get
From above , it is clear that In quadrilateral ABCD , diagonals are equal and they bisect each other at 90° .
? Quadrilateral ABCD is square.
Correct Answer: ?A + 180°
Explanation:
From the given figure, In ?ABC
We know that , Exterior angle = Sum of two interior angles
?1 = ?A + ?5 ................. ( 1 )
and ?2 = ?A + ?6 ................. ( 2 )
Adding equations ( 1 ) and ( 2 ).
?1 + ?2 = 2?A + ?5 + ?6
= 2?A + (180° ? ?A) = ?A + 180°
The given question can be restated as the sum of two exterior angles exceeds ?A of the ?ABC by 2 right angles.
Correct Answer: x = ? + ? + ?
Explanation:
From above figure , we can see that
Join B and D and produce BD to E
Then, p + q = ? and s + t = x
We know that , Exterior angle = Sum of two interior angle
Now, s = p + ? (Exterior angle of a ? prop.)
Similarly, t = q + ? (Exterior angle of a ? prop.)
Adding, s + t = p + q + ? + ?
Putting s + t = x and p + q = ? ,
Hence x = ? + ? + ?
Correct Answer: any triangle
Explanation:
We know that In center of every triangle ( acute , obtuse and right angle ) lies in its interior.
Hence required answer will be any triangle .
Correct Answer: 25 81
Explanation:
Correct Answer: 36?2 m
Explanation:
Correct Answer: 8 cm2
Explanation:
Correct Answer: Bisectors
Explanation:
The circumcentre of a triangle is always the point of intersection of the Bisectors .Hence required answer will be bisectors .
Correct Answer: 4.8 cm
Explanation:
Correct Answer: 154
Explanation:
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