Discussion
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- Question
- 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
- Correct Answer
- Bisectors
ExplanationThe circumcentre of a triangle is always the point of intersection of the Bisectors .Hence required answer will be bisectors .
- 1. 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
- 2. 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
- 3. 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 Discuss
- 4. 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
- 5. 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
- 6. 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
- 7. 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
- 8. In a triangle ABC, the length of the sides AB, AC and BC are 3, 5 and 6 cm respectively. If a point D on BC is drawn such that the line AD bisects the angle A internally, then what is the length of BD?
Options- A. 2 cm
- B. 2.25 cm
- C. 2.5 cm
- D. 3 cm Discuss
- 9. The number of tangents that can be drawn to two non-intersecting circles :
Options- A. 4
- B. 3
- C. 2
- D. 13 Discuss
- 10. X, Y are the mid-points of opposite sides AB and DC of a parallelogram ABCD. AY and DX are joined intersecting in P; CX and BY are joined intersecting in Q. Then PXQY is a :
Options- A. Rectangle
- B. Rhombus
- C. Parallelogram
- D. Square Discuss
Plane Geometry problems
Search Results
Correct Answer: 8 cm2
Explanation:
Correct Answer: 36?2 m
Explanation:
Correct Answer: 5
Explanation:
From 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
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: 4.8 cm
Explanation:
Correct Answer: 154
Explanation:
Correct Answer: 2.25 cm
Explanation:
In a triangle ABC,
Given :- AB = 3 cm , AC = 5 cm and BC = 6 cm
We know that BD : DC = AB : AC
BD : DC = 3 : 5
? Divided BC = 6 in the ratio 3 : 5
BC = 3x + 5x = 6 ? 8x = 6 ? x = 6/8 = 0.75
? BD = 2.25, CD = 3.75.
Correct Answer: 4
Explanation:
We know that when two circle neither touch nor intersect and one lies outside the other, then 4 common tangents can be drawn.
For 4 common tangents , we get
? r1 + r2 < c1c2
Hence ,The number of tangents = 4
Correct Answer: Parallelogram
Explanation:
From above given figure ,
Proceeding as in Q. No. 4, we can prove that AXCY is a parallelogram .
Similarly, BXDY is a parallelogram.
Now, AXCY is a parallelogram .
? AY || CX
[? Opposite sides of a parallelogram are parallel]
? PY || QX ?(1)
Also, BXDY is a parallelogram
? DX || BY [? Opposite sides of a parallelogram are parallel]
? PX || QY ?(2)
Thus, in a quadrilateral PXQY,
From (i) and (ii) ,
we have , PY || QX and PX || QY
? PXQY is a parallelogram.
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