Question and Answers Forum

All Questions      Topic List

Geometry Questions

Previous in All Question      Next in All Question      

Previous in Geometry      Next in Geometry      

Question Number 82878 by mr W last updated on 25/Feb/20

Commented by behi83417@gmail.com last updated on 25/Feb/20

$$\mathrm{Beautiful}\mathrm{quistion}.\mathrm{waiting}\mathrm{for}\mathrm{answer}...$$

Commented by ajfour last updated on 25/Feb/20

$$\mathrm{so}\mathrm{please}\mathrm{answer}\mathrm{Behi}\mathrm{Sir}..$$

Commented by behi83417@gmail.com last updated on 25/Feb/20

$$\mathrm{dear}\mathrm{Ajfour}\mathrm{sir}!\mathrm{i}\mathrm{am}\mathrm{waiting}\mathrm{for}\mathrm{answer}$$$$\mathrm{of}\mathrm{my}\mathrm{master}:\mathrm{mrW}.(\mathrm{also}\mathrm{your}\mathrm{answer}$$$$\mathrm{too},\mathrm{most}\mathrm{welcome}.)$$

Answered by mr W last updated on 26/Feb/20

Commented by mr W last updated on 26/Feb/20

$$\mathrm{\Delta }AFG:$$$$semiperimeter=u$$$$incircleradius=n$$$$excircleradius=a$$$$u=\frac{p+q+s}{2}$$$$n=\frac{{\mathrm{\Delta }}_{AFG}}{u}$$$$\Rightarrow \frac{1}{n}=\frac{u}{{\mathrm{\Delta }}_{AFG}}$$$$a=\frac{{\mathrm{\Delta }}_{AFG}}{u-s}$$$$\Rightarrow \frac{1}{a}=\frac{u-s}{{\mathrm{\Delta }}_{AFG}}$$$$$$$$\mathrm{\Delta }AGE:$$$$semiperimeter=v$$$$incircleradius=b$$$$excircleradius=m$$$$v=\frac{q+r+t}{2}$$$$similarly$$$$\Rightarrow \frac{1}{b}=\frac{v}{{\mathrm{\Delta }}_{AGE}}$$$$\Rightarrow \frac{1}{m}=\frac{v-t}{{\mathrm{\Delta }}_{AGE}}$$$$$$$$\frac{1}{a}+\frac{1}{b}=\frac{u-s}{{\mathrm{\Delta }}_{AFG}}+\frac{v}{{\mathrm{\Delta }}_{AGE}}=\frac{1}{{\mathrm{\Delta }}_{AFG}}(u-s+\frac{{\mathrm{\Delta }}_{AFG}}{{\mathrm{\Delta }}_{AGE}}v)$$$$\Rightarrow \frac{1}{a}+\frac{1}{b}=\frac{1}{{\mathrm{\Delta }}_{AFG}}(u-s+\frac{s}{t}v)$$$$\frac{1}{n}+\frac{1}{m}=\frac{u}{{\mathrm{\Delta }}_{AFG}}+\frac{v-t}{{\mathrm{\Delta }}_{AGE}}=\frac{1}{{\mathrm{\Delta }}_{AFG}}[u+\frac{{\mathrm{\Delta }}_{AFG}}{{\mathrm{\Delta }}_{AGE}}(v-t)]$$$$\frac{1}{n}+\frac{1}{m}=\frac{1}{{\mathrm{\Delta }}_{AFG}}[u+\frac{s}{t}(v-t)]$$$$\Rightarrow \frac{1}{n}+\frac{1}{m}=\frac{1}{{\mathrm{\Delta }}_{AFG}}(u+\frac{s}{t}v-s)$$$$\Rightarrow \frac{1}{a}+\frac{1}{b}=\frac{1}{m}+\frac{1}{n}$$

Commented by ajfour last updated on 28/Feb/20

$$\mathrm{Thanks}\mathrm{sir},\mathrm{what}\mathrm{a}\mathrm{presentation}!$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com