41(Geometry and Mensuration,LOD II,Pg. 212)
Q. Find the ratio of the diameter of the circles inscribed in and circumscribing an equilateral triangle to its height.
(a)1:2:1
(b)1:2:3
(c)1:3:4
(d)3:2:1
The Q. seems very easy.I m not getting any of the option.I think the options are wrong.
My ans d : D : h = 2:4:3
What u say guys?
41(Geometry and Mensuration,LOD II,Pg. 212)
Q. Find the ratio of the diameter of the circles inscribed in and circumscribing an equilateral triangle to its height.
(a)1:2:1
(b)1:2:3
(c)1:3:4
(d)3:2:1
The Q. seems very easy.I m not getting any of the option.I think the options are wrong.
My ans d : D : h = 2:4:3
What u say guys?
The answer should be '2' i.e 1:2:3 . Since the triangle is an equilateral therefore the center of the circumscribing circle and the inscribed the circle lies at the centroid.Let the height of the triangle be '3h'. And since the centroid lies on the median at a distance of '2h' from the vertex (radius of the circumscribing circle) and at a distance of 'h' from the base(radius of the inscribed circle). Therefore the ratio is 1:2:3
Cheers!!!
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The answer should be '2' i.e 1:2:3 . Since the triangle is an equilateral therefore the center of the circumscribing circle and the inscribed the circle lies at the centroid.Let the height of the triangle be '3h'. And since the centroid lies on the median at a distance of '2h' from the vertex (radius of the circumscribing circle) and at a distance of 'h' from the base(). Therefore the ratio is 1:2:3
Cheers!!!
Here the Question Say's Ratio of the Diameter not Radius
We know in case of equilateral triangle
h=(3*a)/2 .
R=a/3 => D=2a/3
r=a/(2*3) = > d=a/3
T.f. d : D : h=a/3 :2a/3 :(3*a)/2
=2 : 4 :3
Even doin simply by ur way the ans is same 2 : 4 :3
What u say?
regards
mejogi
Here the Question Say's Ratio of the Diameter not Radius
We know in case of equilateral triangle
h=(3*a)/2 .
R=a/3 => D=2a/3
r=a/(2*3) = > d=a/3
T.f. d : D : h=a/3 :2a/3 :(3*a)/2
=2 : 4 :3
Even doin simply by ur way the ans is same 2 : 4 :3
What u say?
regards
mejogi
The ratio between radius or the diameter is always same...
And Moreover, we both are using the same methods.
h=(3*a)/2 .
R = 2h/3 = a/ 3
r=h/3 = a/23
You ain't using the correct formula. Hence, the ratios are 1:2:3
But if u consider constant ratios then answer will be 2:4:3.
and if u r considering radius then answer will be option b.
But if u consider constant ratios then answer will be 2:4:3.
and if u r considering radius then answer will be option b.
i cant draw the question;so plz refer to GEOMETRY LOD-II Q.18
if two equal circles of rad.5 cm have 2 common tangent AB & CD whih touch the circle on A,C,B and D respectively and if CD=24 cm, find the length of AB.
( for those who dnt hav d figure, AB is direct common tangent & CD is tranverse common tangent )
a. 27 cm b. 25 cm c. 26 cm d. 30 cm
i cant draw the question;so plz refer to GEOMETRY LOD-II Q.18
if two equal circles of rad.5 cm have 2 common tangent AB & CD whih touch the circle on A,C,B and D respectively and if CD=24 cm, find the length of AB.
( for those who dnt hav d figure, AB is direct common tangent & CD is tranverse common tangent )
a. 27 cm b. 25 cm c. 26 cm d. 30 cm
option (c) is the ans.
as it is a transverse tangent ....24^2 = dist betw centers^2 - 10^2
Option (C)
ive attatched the dig along with it .
Consider triangle PCS and SDQ.
By AAA Theorm these 2 triangles are similar .Therfore the ratio of sides will be equal.
DQ/PC = QS/PS .Therefore QS=PS .Hence PS=12
now, clearly PS=13 ,PQ=26=AB
Few questions from Time and speed ..LOD2
Q1>Abus left point X for point Y , 2hrs later a car left X for Y and arrived at Y at the same time as the bus.If the car and bus left from oppo. ends simeltaneously ,they wud meet 1.33 hrs after the start . How much time did it take the bus to travel from X to Y.
(a)2hrs (b)4hrs (c)6hrs (d)8hrs
Q2>An ant moved for several secs and covered 3mm in the 1st sec and 4mm in each successive second than its predecessor.If the ant had covered 1mm in the 1st sec and 8mm more in each successive sec ,then the difference between the path it wud cover during same time and actual path wud b more than 6mm but less than 30mm. Find the time for which the ant moved.
(a)5s (b)4s (c)6s (d)non of these
Q3>Ravi who lives in the countryside ,caught a train for home earlier than usual , yesterday.Hs wife normally drives to the station to meet him,but yesterday he set out on foot from the station to meet his wife on the way.He reached home 12 mins earlier than he wud have done had he waited at the station for his wife .The car travels at a uniform speed , which is 5 times Ravi's speed on foot. Ravi reached home at exactly 6 o'clock.At what time wud he have reached home if his wife forewarne of his plan had met at the station?
(a)5:48 (b)5:24 (c)5:00 (d)5:36
Do post ur method too............. 😃 happy solving
Option (C)
ive attatched the dig along with it .
Consider triangle PCS and SDQ.
By AAA Theorm these 2 triangles are similar .Therfore the ratio of sides will be equal.
DQ/PC = QS/PS .Therefore QS=PS .Hence PS=12
now, clearly PS=13 ,PQ=26=AB
Hey plz check the bold part....it shud b CS=12:)
ya ans. is (C) 26 cm
thnx
Bhayanak Maut SaysHey plz check the bold part....it shud b CS=12:)
PS = CS 😃 already proved by simillar triangle method
cloudsonfire SaysPS = CS 😃 already proved by simillar triangle method
Hey how can PS=CS?:neutral:
Nwys i got the soln.:)
Hey how can PS=CS?:neutral:
Nwys i got the soln.:)
sorry sorry got ur point .........typo mistake 😞
Q1>Abus left point X for point Y , 2hrs later a car left X for Y and arrived at Y at the same time as the bus.If the car and bus left from oppo. ends simeltaneously ,they wud meet 1.33 hrs after the start . How much time did it take the bus to travel from X to Y.
(a)2hrs (b)4hrs (c)6hrs (d)8hrs
bt=c(t-2)=4/3*(b+c)=d
t=4
answer b
It should be after 6'o clock am i missing something
Q3>Ravi who lives in the countryside ,caught a train for home earlier than usual , yesterday.Hs wife normally drives to the station to meet him,but yesterday he set out on foot from the station to meet his wife on the way.He reached home 12 mins earlier than he wud have done had he waited at the station for his wife .The car travels at a uniform speed , which is 5 times Ravi's speed on foot. Ravi reached home at exactly 6 o'clock.At what time wud he have reached home if his wife forewarne of his plan had met at the station?
(a)5:48 (b)5:24 (c)5:00 (d)5:36
bt=c(t-2)=4/3*(b+c)=d
t=4
answer a
It should be after 6'o clock am i missing something :neutral:
ans to 1st question is 4hrs .
cloudsonfire Saysans to 1st question is 4hrs .
yeah
just picked the wrong option u can see t=4:)
bt=c(t-2)=4/3*(b+c)=d
t=4
answer b
It should be after 6'o clock am i missing something :neutral:
@krishvik
im still not able to reach the answer for this question , can u elaborate on this .....
bt=c(t-2)=4/3*(b+c)=d
t=4
answer b
and ppl wat abt the other questions????? 😞
The ratio between radius or the diameter is always same...
And Moreover, we both are using the same methods.
h=(3*a)/2 .
R = 2h/3 = a/ 3
r=h/3 = a/23
You ain't using the correct formula. Hence, the ratios are 1:2:3
Hi,abhijit
See, I know that the ratio of Diameters and radius is sames.But when a third variable comes then we can't reduce ratio of the first 2 variables and divide it by third variable to get the ratio of these three variables.So don't reduce the ratio of diameters alone before putting it with the height.(Plz refer to ratio and Proportion(A.S. Pg. 122 last 5 lines) or visit offcial CAT 2007 thread for more,I have posted the same Q. there and got the same ans,as i did)
regards
mejogi