Show that aq= 1/2 perimeter of triangle abc, Mathematics

Assignment Help:

A circle touches the side BC of a triangle ABC at P and touches AB and AC when produced at Q and R.

Show that AQ= 1/2 (perimeter of triangle ABC)

Ans:    Since the length of tangents from external point to a circle are equal.

AQ = AR BQ = BP PC = CR

Since  AQ = AR

AB + BQ = AC + CR

∴ AB + BP = AC + PC (Since BQ = BP & PC = CR)

Perimeter of ? ABC = AB + AC + BC

= AB + BP + PC + AC

= AQ + PC + AC (Since AB + BP = AQ)

= AQ + AB + BP (Since PC + AC = AB + BP)

= AQ + AQ (Since AB + BP = AQ)

Perimeter of ? ABC = 2AQ

∴ AQ = 1/2 (perimeter of triangle ABC)


Related Discussions:- Show that aq= 1/2 perimeter of triangle abc

Homework, How do you simplify 10:30:45

How do you simplify 10:30:45

Indicestitle.., Advantages and disadvantages of paasche indices

Advantages and disadvantages of paasche indices

Fractions, Mr. And Mrs. samuel visited Florida and purchased 120 oranges. ...

Mr. And Mrs. samuel visited Florida and purchased 120 oranges. They gave 1/4 of them to relatives, ate 1/12 of them in the hotel, and gave 1/3 of them to friends. The shipped the

Example of parametric equations and parametric curves, Draw the parametric ...

Draw the parametric curve for the subsequent set of parametric equations. X = t 2 +t Y=2t-1 -1 t 1 Solution Note that the only dissimilarity here is the exis

Profit, A wholesaler allows a discount of 20% on the list price to a retail...

A wholesaler allows a discount of 20% on the list price to a retailer. The retailer sells at 5% discount on the list price.If a customer paid Rs 114 for an article,what profit is m

Determine the team having similar code-pigeon hole principle, Shirts number...

Shirts numbered consecutively from 1 to 20 are worn by 20 members of a bowling league. While any three of these members are selected to be a team, the league aims to use the sum of

Surface area of prisms , Can you help me find out how to find the surface a...

Can you help me find out how to find the surface area of a prism

Math, The Timbuktu post office has only 3 cents and 7 cents stamps having r...

The Timbuktu post office has only 3 cents and 7 cents stamps having run out of all other denominations. What are the six amounts of postage that cannot be created? How do you know

What is the square root of -i, To find sq root by the simple step... root (...

To find sq root by the simple step... root (-i)=a+ib............... and arg of -i= -pi/2 or 5pi/2

NUMERABILITY, AFIGURE THIS OUT(3) (14) (17) (20) (25)= 8 WHAT ARE THE PROC...

AFIGURE THIS OUT(3) (14) (17) (20) (25)= 8 WHAT ARE THE PROCEDURES (-)(+)(x)(div) BETWEEN EACH NUMBER TO COME UP WITH 8 ?sk question #Minimum 100 words accepted#

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