Prove the parallelogram circumscribing a circle is rhombus, Mathematics

Prove that the parallelogram circumscribing a circle is rhombus.

1224_circle.png

Ans   Given : ABCD is a parallelogram circumscribing a circle.

To prove : - ABCD is a rhombus or

AB=BC=CD=DA

Proof: Since the length of tangents from external are equal in length

∴AS = AR       .....(1)

BQ = BR      .....(2)

QC = PC      .....(3) SD = DP           .....(4)

Adding (1), (2), (3) & (4).

AS + SD + BQ + QC = AR + BR + PC + DP AD + BC = AB + DC

AD + AD = AB + AB

Since BC = AD & DC = AB (opposite sides of a parallelogram are equal)

2AD = 2AB

∴AD = AB      .....(5)

BC = AD (opposite sides of a parallelogram)

DC = AB        .....(6) From (5) and (6)

AB = BC = CD = DA Hence proved

Posted Date: 4/10/2013 4:03:15 AM | Location : United States







Related Discussions:- Prove the parallelogram circumscribing a circle is rhombus, Assignment Help, Ask Question on Prove the parallelogram circumscribing a circle is rhombus, Get Answer, Expert's Help, Prove the parallelogram circumscribing a circle is rhombus Discussions

Write discussion on Prove the parallelogram circumscribing a circle is rhombus
Your posts are moderated
Related Questions
Decision Theory Decisions There are many types of decision making 1.      Decision making under uncertainty It refer to situations where more than one outcome can r

Determine Rank Correlation Coefficient A group of 8 accountancy students are tested in Quantitative Techniques and Law II.  Their rankings in the two tests were as:


let setM={X,2X,4X} for any numberX .if average (arthemetic mean)of the number in setM is 14.what is the value of X?

Find out the domain of each of the following.  (a) f (x,y) = √ (x+y) (b) f (x,y) = √x+√y  (c) f (x,y) = ln (9 - x 2 - 9y 2 ) Solution (a) In this example we know

Apply depth-first-search to find out the spanning tree for the subsequent graph with vertex d as the starting vertex.        Ans: Let us begin with node'd'. Mark d as vi

#question application of vector and scalar in our daily life

Multiple Linear Regression Models There are situations whether there is more than one factor which influence the dependent variable Illustration Cost of production weekl

greens function for x''''=0, x(1)=0, x''(0)+x''(1)=0 is G(t,s)= {1-s for t or equal to s

Any 15 foot ladder is resting against the wall. The bottom is at first 10 feet away from the wall & is being pushed in the direction of the wall at a rate of 1 ft/sec. How rapid is