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

Houses having the floor , Suppose you are in the market for a new home and ...

Suppose you are in the market for a new home and are interested in a new housing community under construction in a another city. a) The sales representative informs you that the

Pair of straight lines, how to solve the problems? methods to solve the que...

how to solve the problems? methods to solve the question of joint lines

Money, What is the formulate of finding commission

What is the formulate of finding commission

Daily revenue for next 30 days, Owner of a computer repair shop has daily r...

Owner of a computer repair shop has daily revenue with mean $7200 and SD $1200 Daily revenue for next 30 days will be monitored. What is probability that daily revenue for those 30

Fundamental theorem of integral facts , Fundamental Theorem of Calculus, Pa...

Fundamental Theorem of Calculus, Part II  Assume f(x) is a continuous function on [a,b] and also assume that F(x) is any anti- derivative for f(x). Hence, a ∫ b f(x) dx =

Which expression below is equal to 5, Which expression below is equal to 5?...

Which expression below is equal to 5? The correct order of operations must be used here. PEMDAS tells you in which you should do the operations in the subsequent order: Pare

Algebra, Evaluate: 30 - 12÷3×2 =

Evaluate: 30 - 12÷3×2 =

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