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- Question
- The number of tangents that can be drawn to two non-intersecting circles :
Options- A. 4
- B. 3
- C. 2
- D. 13
- Correct Answer
- 4
ExplanationWe 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 - 1. 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
- 2. 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
- 3. 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
- 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
- 5. 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
- 6. 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
- 7. ABCD is a rhombus with ? ABC = 56°, then ? ACD is equal to :
Options- A. 90°
- B. 60°
- C. 56°
- D. 62° Discuss
- 8. The diagonals of a rectangle ABCD meet at 0. If ? BOC = 44°, then ? OAD is equal to :
Options- A. 90°
- B. 60°
- C. 100°
- D. 68° Discuss
- 9. In the given figure, In a ? ABC , ?B = ? C. If AM is the bisector of ? BAC and AN ? BC, then ? MAN is equal to :
Options- A. 1 (?B + ?C) 2
- B. 1 (?C- ?B ) 2
- C. ?B + ?C
- D. 1 (?B - ?C) 2 Discuss
- 10. If H is the orthocentre of ? ABC, then the orthocentre of ? HBC is (fig. given) :
Options- A. N
- B. M
- C. A
- D. L Discuss
Plane Geometry problems
Search Results
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: 154
Explanation:
Correct Answer: 4.8 cm
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: 8 cm2
Explanation:
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.
Correct Answer: 62°
Explanation:
Correct Answer: 68°
Explanation:
Correct Answer: 1 (?B - ?C) 2
Explanation:
Correct Answer: M
Explanation:
From above given triangle , It is clear that the altitudes AL, BM and CN of ?ABC intersect at H. Then H is the orthocentre of ?ABC.
In ?ABC, HL ? BC and BN ? CH.
Thus, the two altitudes HL and BN of ?HBC, intersects at A.
Hence the orthocentre of ?HBC is M .
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