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

Decision-making under conditions of uncertainty, Decision-Making Under Cond...

Decision-Making Under Conditions of Uncertainty With decision making under uncertainty, the decision maker is aware of different possible states of nature, but has insufficient

Probability: determine the optimal strategy , On a picnic outing, 2 two-pe...

On a picnic outing, 2 two-person teams are playing hide-and-seek. There are four  hiding locations (A, B, C, and D), and the two members of the hiding team can hide separately in a

Shares and dividends, how to see shares and dividends of a company and are ...

how to see shares and dividends of a company and are they seen day wise?

Tests for an ideal index number, Tests for an Ideal Index Number 1. F...

Tests for an Ideal Index Number 1. Factor Reversal Test Factor Reversal Test indicates that when the price index is multiplied along with a quantity index that is factors

Shares and dividends, to use newspaperto study and report on shares and div...

to use newspaperto study and report on shares and dividend

Identify the flaw in the argument, Identify the flaw in the following argum...

Identify the flaw in the following argument which supposedly determines that n 2 is even when n is an even integer. As well name the reasoning:             Assume that n 2 is

Shiites muhammad''s flight from mecca to medina, The first year of the Isla...

The first year of the Islamic calendar marks the following event: The birth of Muhammad The Qu'ran is assembled into a single sacred text The division of the Sunnis and the Shiites

How many people should she expect not to show, Laura is planning her weddin...

Laura is planning her wedding. She expects 230 people to attend the wedding, but she has been told that around 5% typically don't show. About how many people should she expect not

Probability, An unbiased die is tossed twice .Find the probability of getti...

An unbiased die is tossed twice .Find the probability of getting a 4,5,6 on the first toss and a 1,2,3,4 on the second toss

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