Plane Geometry problems
- 1. 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
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
- 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
Correct Answer: 36?2 m
Explanation:
- 3. 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
Correct Answer: 8 cm2
Explanation:
- 4. 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
Correct Answer: Bisectors
Explanation:
The circumcentre of a triangle is always the point of intersection of the Bisectors .Hence required answer will be bisectors .
- 5. 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
Correct Answer: 4.8 cm
Explanation:
- 6. 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
Correct Answer: 154
Explanation:
- 7. 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
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.
- 8. The number of tangents that can be drawn to two non-intersecting circles :
Options- A. 4
- B. 3
- C. 2
- D. 13 Discuss
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
- 9. 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
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.
- 10. ABCD is a rhombus with ? ABC = 56°, then ? ACD is equal to :
Options- A. 90°
- B. 60°
- C. 56°
- D. 62° Discuss
Correct Answer: 62°
Explanation:
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