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

Geometry, In a square of side 8 cm two quadrant with taking the side of squ...

In a square of side 8 cm two quadrant with taking the side of square as radius are inscribed in the square..

Patrice has worked a certain how many hours has she worked, Patrice has wor...

Patrice has worked a certain amount of hours so far this week. Tomorrow she will work four more hours to finish out the week along with a total of 10 hours. How many hours has she

Decision theory, DECISION THEORY People constantly make decision...

DECISION THEORY People constantly make decisions in their private lives as well as in their work. Some decisions are qualitative in terms of their implications and signi

integral 0 to pi e^cosx cos (sinx) dx, Let u = sin(x). Then du = cos(x) dx...

Let u = sin(x). Then du = cos(x) dx. So you can now antidifferentiate e^u du. This is e^u + C = e^sin(x) + C.  Then substitute your range 0 to pi. e^sin (pi)-e^sin(0) =0-0 =0

Parabola, If the point (a,2a) is an interior point of the region bounded by...

If the point (a,2a) is an interior point of the region bounded by the parabola y2=16x and the double ordinate through the focus then a belongs to

Test of hypothesis about the difference among two means, Test of hypothesis...

Test of hypothesis about the difference among two means The t test can be utilized under two assumptions when testing hypothesis about the difference among the two means; that

Solving a system of 2 equations addition-subtraction method, Solving a Syst...

Solving a System of 2 Equations Using the Addition/Subtraction Method To solve a system of linear equations using the addition/subtraction method, both equations should first b

Doubles Plus 1 and Doubles Minus 1, Write the doubles fact you used to solv...

Write the doubles fact you used to solve the problem. 7 + 8 = 15

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