Prove the parallelogram circumscribing a circle is rhombus, Mathematics

Assignment Help:

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


Related Discussions:- Prove the parallelogram circumscribing a circle is rhombus

Nemeric patterns, Kelli calls her grandmother every month. Every other mont...

Kelli calls her grandmother every month. Every other month,Kelli also calls her cousin in January, how many calls will Kelli have made to her grandmother and her cousin by the end

How many teachers are there at russell high, There are 81 women teachers at...

There are 81 women teachers at Russell High. If 45% of the teachers in the school are women, how many teachers are there at Russell High? Use the proportion part/whole = %/100.

Find a power series representation for the function, Find a power series re...

Find a power series representation for the subsequent function and find out its interval of convergence. g (x) = 1/1+x 3 Solution What we require to do here is to rela

Example of addition of signed numbers, Example of addition of Signed Number...

Example of addition of Signed Numbers: Example: (-2) + 3 + 4 = 0 - 2 + 3 + 4 Solution: Thus: (-2) + 3 + 4 = 5  Example: 10 + (-5) + 8 + (-7)

Write down two more reasons why division is difficult, Write down two more ...

Write down two more reasons why children consider 'division' difficult. Regarding the first reason given above, one of fie few division related experiences that the child perhaps d

Area between two curves, Area between Two Curves We'll start with the ...

Area between Two Curves We'll start with the formula for finding the area among y = f(x) and y = g(x) on the interval [a,b].  We will also suppose that f(x) ≥ g(x) on [a,b].

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd