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

What is the greatest value of the number, Five more than the quotient of a ...

Five more than the quotient of a number and 2 is at least that number. What is the greatest value of the number? Let x = the number. Notice that quotient is a key word for div

Online tutoring, how can i find the online students ?

how can i find the online students ?

Find the angle of elevation, A 50-foot pole casts a shadow on the ground. ...

A 50-foot pole casts a shadow on the ground. a) Express the angle of elevation θ of the sun as a function of the length s of the shadow. (Hint you may wish to draw this firs

Making connections with maths, MAKING CONNECTIONS :  you have read about w...

MAKING CONNECTIONS :  you have read about what the ability to think mathematically involves. In this section we shall discuss ways of developing this ability in children. As yo

Fractions, what is equizilent to 2/5

what is equizilent to 2/5

The limit, The Limit : In the earlier section we looked at some problems ...

The Limit : In the earlier section we looked at some problems & in both problems we had a function (slope in the tangent problem case & average rate of change in the rate of chan

Important points about the alternating series test, Important Points About ...

Important Points About the Alternating Series Test There are a several things to note about this test.  Very first, unlike the Integral Test and the Comparison or Limit Compari

Regrouping, in regrouping if we have abig number in the end what should i d...

in regrouping if we have abig number in the end what should i do?add an number on top of it,please help

Simpson rule - approximating definite integrals, Simpson's Rule - Approxima...

Simpson's Rule - Approximating Definite Integrals This is the last method we're going to take a look at and in this case we will once again divide up the interval [a, b] int

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