Request a call back

Join NOW to get access to exclusive study material for best results

CBSE Class 10 Answered

If all sides of a parallelogram touch a circle,prove that the parallelogram is a rhombus
Asked by | 29 Feb, 2008, 03:08: PM
answered-by-expert Expert Answer

 

 

 

 

Solution

 Given

Parallelogram ABCD touches a circle with centre O.
To prove
ABCD is a rhombus.
 
Proof
 Since the length of the tangents from an external point to a given circle are equal
So,
AP=AS           (i)
BP=BQ           (ii)
CR=CQ and  (iii)
DR=DS          (iv)
 
Adding (i), (ii),(iii),(iv) we get
(AP+BP)+(CR+DR)=(AS+DS)+(BQ+CQ)
AB+CD=AD+BC
Since ABCD is a Parallelogram CD=AB and BC=AD
This implies, AB+AB=AD+AD
2AB=2AD
This implies AB=AD
But AB=CD and AD=BC as opposite sides of a Parallelogram are equal.
Therefore , AB=BC=CD=AD.
Hence ABCD is a rhombus.

 

 

Answered by | 29 Feb, 2008, 04:09: PM
CBSE 10 - Maths
Asked by sheetal.kolte | 15 Mar, 2024, 03:25: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by rajk7371198 | 09 Feb, 2024, 11:55: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by mp2235793 | 11 Jan, 2024, 10:31: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by lakshmimanjula433 | 19 Nov, 2023, 10:50: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by latayadav23 | 14 Oct, 2023, 12:49: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
kk
question image
Asked by 096karan | 04 Jan, 2023, 02:53: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by krnishant027 | 18 Sep, 2020, 01:37: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by technicalboy43 | 17 Mar, 2020, 08:47: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
Get Latest Study Material for Academic year 24-25 Click here
×