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Solve geometry question
by Abhishek Sharma - Thursday, 16 August 2012, 06:42 PM
 

Hi

In the attched image,

In the figure, the square and the circle are intersecting each other such that AB = BC. If the radius of the circle, with the centre as O, is 1 unit and OB = 1/2, then find the length of AB.

Thanks

 


Re: Solve geometry question
by Abhishek Sharma - Thursday, 16 August 2012, 06:44 PM
 

Question 2

P is a point inside rectangle ABCD such that AP = 4 units, BP = 3 units and PD = 5 units. Find the length of PC.

 


Re: Solve geometry question
by Abhishek Sharma - Thursday, 16 August 2012, 06:47 PM
 

Question 3

 


Re: Solve geometry question
by Mohit Sharma - Thursday, 16 August 2012, 07:33 PM
  Hi abhishek,
Since AB and BC are equal they are equidistant from center O. In that case the perpendicular distance between center O and AB will be 1/2sqrt(2).
Since radius is 1 unit. applying Pythagoras theorem here will do our work and final ans will be.
(7+1)/2sqrt(2).
Thanks,
Re: Solve geometry question
by Mohit Sharma - Thursday, 16 August 2012, 07:34 PM
  We have a formula,
AP^2+CP^2=BP^2+DP^2
PC=3sqrt(2)
Thanks,
Re: Solve geometry question
by Mohit Sharma - Thursday, 16 August 2012, 07:40 PM
  Solution to this question is length.
Join the centers of the circles draw perpendiculars to the base. From the center of the smaller triangle draw a line perpendicular to the line drawn towards the base from the big circle.
A triangle will be formed which will be similar to the main triangle.
pythagoras triplet of (3,4,5) will be formed solve it for bigger triangle by using AB, BC and CA as tangents to the circle.
Ans will be AB= 21/2.

PS. let me know if any ans is wrng.

Thanks,
Re: Solve geometry question
by Abhishek Sharma - Thursday, 16 August 2012, 08:34 PM
 

Hi Mohit

thanks for quick solutions

The answer for the third one is incorrect.The options are as follows:

A)12 B)32 C)41 D)152/3

Also explain that using tengents how to do it because i am not getting the answer?

Re: Solve geometry question
by rakshit surana - Thursday, 16 August 2012, 09:23 PM
  12??
done wd tangents
Re: Solve geometry question
by Abhishek Sharma - Thursday, 16 August 2012, 09:40 PM
 

yes

please explain.

Re: Solve geometry question
by rakshit surana - Friday, 17 August 2012, 12:26 AM
  let AB be x and where bigger circle touch AB be E , BC be F , AC be G and where small circle touch side BC be H and AC be I

now FH = GI = length of direct tangent = root ( (4+1)^2 - (4-1)^2) = 4 cm
BF = 4 cm ( radius of traingle)
so BE will also be 4 cm by tangent property
so AE = x-4 = AG
let CH = CI = y cm
applying pytha.
x^2 + (8+y)^2 = (x+y)^2
64 +16y = 2xy
32 = y(x-8)
now wrking wid options
32 = 8*4
x= 16 not in options
x = 12 done !!!!!!!!!!
Re: Solve geometry question
by Abhishek Sharma - Monday, 20 August 2012, 02:20 AM
 

Hi

Please solve foll geometry questions:

CD is perpendicular to chord AB. Find the radius of the circle.

 


Re: Solve geometry question
by Abhishek Sharma - Monday, 20 August 2012, 02:21 AM
 

Hi

The length of the side of the square is 2. Find the radius of the smaller circle?

 


Re: Solve geometry question
by Abhishek Sharma - Monday, 20 August 2012, 02:22 AM
 

Another one

All three sides of a triangle have integer side lengths of 11, 60 and n cm. For how many values of n is the triangle acute-angled?

Options

3,6,5,2

Re: Solve geometry question
by Karan Jaikant - Monday, 20 August 2012, 06:02 PM
  The radius of the smaller circle = 4 - 2√3
Re: Solve geometry question
by Abhishek Sharma - Monday, 20 August 2012, 07:53 PM
 

Please solve foll Question

Kamal Sir Please help

1.In rectangle ABCD, the perpendicular bisector of AC divides the longer side AB in a ratio 2:1. Then, the degree measure of the angle between AC and BD is

 A)30 B)45 C)60 D)90

2.

In a trapezium, the line joining the midpoints of the diagonals is 2 cm long. If the longer base is 48 cm long, then the length of the shorter base is

 a)36 b)44 c)20 d)40

 

Re: Solve geometry question
by TG Team - Monday, 20 August 2012, 08:02 PM
 

Hi Abhishek smile

Just use the condition that c2 < a2 + b2 to confirm whether triangle is acute angled. Here c is the longest side of the triangle.

So two cases are possible i.e. either 60 is the longest side or n is the longest side. Just find the values of n satisfying that conditions.

Re: Solve geometry question
by TG Team - Monday, 20 August 2012, 08:03 PM
 

1. 60

2. 44

Re: Solve geometry question
by Gautam Choudhary - Monday, 20 August 2012, 08:04 PM
  65/6
Re: Solve geometry question
by Gautam Choudhary - Monday, 20 August 2012, 09:01 PM
  Is it right-65/6
Re: Solve geometry question
by Abhishek Sharma - Monday, 20 August 2012, 10:43 PM
 

Yes it is.

Could you please share the method by which u solved?

I also got the same answer by using the equation of circle.

How did u do?

Re: Solve geometry question
by Abhishek Sharma - Monday, 20 August 2012, 10:44 PM
 

Hi Kamal,

Answers are obviously correct but please explain.

Re: Solve geometry question
by Gautam Choudhary - Monday, 20 August 2012, 11:47 PM
  Extend dc to meet circle at e ce=ac into cb by dc.then draw two diameters that are perpendicular to each other and the given chords.then look for a right triangle with radius as the hyp. Can u please explain ur method
Re: Solve geometry question
by Gautam Choudhary - Wednesday, 22 August 2012, 02:19 AM
  How did u do it man
Re: Solve geometry question
by Abhishek Sharma - Wednesday, 22 August 2012, 11:27 PM
 

I solved it by using the circle's equation

(x-k)^2+(y-j)^2=r^2 by getting the three points on the circumference of the circle.By the way,What u told i didnt get.

Re: Solve geometry question
by avinash Singh - Monday, 11 August 2014, 09:32 AM
  answer is 20/3.
Re: Solve geometry question
by TG Team - Friday, 12 September 2014, 03:08 PM
  Hi Avinash smile

How did you get this answer? Please show your approach.

Kamal Lohia
Re: Solve geometry question
by abhishek khurana - Thursday, 12 March 2015, 12:02 AM
  20
Re: Solve geometry question
by sivasis dash - Wednesday, 22 July 2015, 10:53 AM
 

answer is 3√3(√3+1)

Please go to the link below to see the answer

 

https://www.quora.com/Triangle-ABC-is-a-right-angled-triangle-right-angled-at-B-A-circle-of-radius-4-cm-lies-inside-the-triangle-and-touches-the-3-sides-of-the-triangle-Another-circle-with-radius-1-cm-lies-inside-the-triangle-but-outside-the-first-circle-The-second-circle-touches-the-first-circle-and-touches-the-sides-AC/answer/Sivasis-Dash

Re: Solve geometry question
by sivasis dash - Wednesday, 22 July 2015, 11:21 AM
  the answer is (_/7 + 1)/2root(2).
Re: Solve geometry question
by sivasis dash - Wednesday, 22 July 2015, 11:34 AM
  Radius of smaller circle is 8-4root(3)/2.
Re: Solve geometry question
by Jay Madhani - Friday, 7 August 2015, 11:09 PM
  (Root(7) + 1 ) / (2 root(2))
Re: Solve geometry question
by bharani venkatesh - Wednesday, 13 July 2016, 11:51 AM
  is the ans (7^1/2 + 1)/ (2*2^1/2) ?
Re: Solve geometry question
by bharani venkatesh - Wednesday, 13 July 2016, 01:55 PM
  3*1.414=4.242