Discussion
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- Question
If the lengths of two parallel chords in a circle of radius 10 cm are 12 cm and 16 cm, then what is the distance between these two chords?
Options- A. 1 cm or 7 cm
- B. 2 cm or 14 cm
- C. 3 cm or 21 cm
- D. 4 cm or 28 cm
- Correct Answer
- 2 cm or 14 cm
- 1. What is the percentage decrease in the area of a triangle if its each side is halved?
Options- A. 75%
- B. 50%
- C. 25%
- D. No change Discuss
- 2. Consider the following statements: 1) The perimeter of a triangle is greater than the sum of its three medinas. 2) In any triangle ABC, if D is any point on BC, then AB + BC + CA > 2AD. Which of the above statements is/are correct?
Options- A. 1 only
- B. 2 only
- C. Both 1 and 2
- D. Neither 1 nor 2 Discuss
- 3. In a circle of radius 8 cm, AB and AC are two chords such that AB = AC = 12 cm. What is the length of chord BC?
Options- A. 2?6 cm
- B. 3?6 cm
- C. 3?7 cm
- D. 6?7 cm Discuss
- 4. ABCD is a quadrilateral with AB = 9 cm, BC = 40 cm, CD = 28 cm, DA = 15 cm and angle ABC is a right ?angel. What is the area of triangle ADC?
Options- A. 126 SQ.CM
- B. 124 SQ.CM
- C. 122 SQ.CM
- D. 120 SQ.CM Discuss
- 5. In ?PQR, ?QPR = 45° and the bisectors of ?PQR and ?PRQ meets at O. What is the value (in degrees) of ?QOR?
Options- A. 107.5
- B. 112.5
- C. 117.5
- D. 122.5 Discuss
- 6. The co-ordinates of the centroid of a triangle ABC are (-1 , 4). What are the co-ordinates of vertex C if co-ordinates of A and B are (-3 , -1) and (3 , 5) respectively?
Options- A. (-3 , 8)
- B. (3 , 8)
- C. (-3 , -8)
- D. (3 , -8) Discuss
- 7. What is the reflection of the point (-4, 3) in the line x = -2?
Options- A. (-4 , -7)
- B. (4 , 3)
- C. (0 , 3)
- D. (-4 , 7) Discuss
- 8. ?XYZ is similar to ?PQR. If ratio of Perimeter of ?XYZ and Perimeter of ?PQR is 4:9 and if PQ = 27 cm, then what is the length of XY (in cm)?
Options- A. 9
- B. 12
- C. 16
- D. 15 Discuss
- 9. The surface area of a sphere is 5544 sq.cm. Find its diameter (in cm).
Options- A. 42
- B. 21
- C. 84
- D. 63 Discuss
- 10. The diagonal of a square is equal to the side of an equilateral triangle. If the area of the square is 15?3 sq cm, what is the area of the equilateral triangle?
Options- A. 45/?2 sq cm
- B. 45?2 sq cm
- C. 45 sq cm
- D. 45/2 sq cm Discuss
Volume and Surface Area problems
Search Results
Correct Answer: 75%
Explanation:
Area of triangle of = ½*a*b* sin? = A
Where a and b are sides of the triangle and ? be the angle between them
After decreasing each side
New area = ½*(a/2)*(b/2)*sin? = ¼ A
%decrease = [(A?¼ A)/A ]*100 = 75%
Correct Answer: Both 1 and 2
Explanation:
Let ABC be the triangle and D. E and F are midpoints of BC, CA and AB respectively.
Recall that the sum of two sides of a triangle is greater than twice the median bisecting the third side,(Theorem to be remembered)
Hence in ?ABD, AD is a median
?
AB + AC > 2(AD)
Similarly, we get
BC + AC > 2CF
BC + AB > 2BE
On adding the above inequations, we get
(AB + AC) + (BC + AC) + (BC + AB )> 2AD + 2CD + 2BE
2(AB + BC + AC) > 2(AD + BE + CF)
?
AB + BC + AC > AD + BE +CF
2.
To prove: AB + BC + CA > 2AD
Construction: AD is joined
Proof: In triangle ABD,
AB + BD > AD [because, the sum of any two sides of a triangle is always greater than the
third side]
----
1
In triangle ADC,
AC + DC > AD [because, the sum of any two
sides of a tri
angle is always greater than the
third side]
----
2
Adding 1 and 2 we get,
AB + BD + AC + DC > AD + AD
=> AB + (BD + DC) + AC > 2AD
=> AB + BC + AC > 2AD
Hence proved
Correct Answer: 6?7 cm
Correct Answer: 126 SQ.CM
Correct Answer: 112.5
Correct Answer: (-3 , 8)
Correct Answer: (0 , 3)
Correct Answer: 12
Correct Answer: 42
Correct Answer: 45/2 sq cm
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