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

Write down a game each for teach maths to children, Write down a game each ...

Write down a game each to teach children i) multiplication, ii) what a circle is, iii) estimation skills. Also say what you expect the child to know before you try to t

Absolute convergence - sequences and series, Absolute Convergence Whil...

Absolute Convergence While we first talked about series convergence we in brief mentioned a stronger type of convergence but did not do anything with it as we didn't have any

Evalute right-hand limit, Evaluate following limits. Solution ...

Evaluate following limits. Solution Let's begin with the right-hand limit.  For this limit we have, x > 4  ⇒          4 - x 3   = 0      also, 4 - x → 0  as x → 4

Parametric curve - parametric equations & polar coordinates, Parametric Cur...

Parametric Curve - Parametric Equations & Polar Coordinates Here now, let us take a look at just how we could probably get two tangents lines at a point.  This was surely not

Exercise of concrete operational stage, Which of the following statements d...

Which of the following statements do you think are true about children? Indicate with 'T' for true and for false. Give reasons for your choice. a) Most primary school children a

Probability, an insurance salesman sells policies to 5 men, all of identica...

an insurance salesman sells policies to 5 men, all of identical age in good health. the probability that a man of this particular age will be alive 20 years hence is 2/3.Find the p

Prime Ideals, Given a standard 2x3 matrix show the ideal formed by the 2x2 ...

Given a standard 2x3 matrix show the ideal formed by the 2x2 minors is Prime.

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