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 185774 by cherokeesay last updated on 27/Jan/23

Answered by HeferH last updated on 27/Jan/23

Commented by HeferH last updated on 27/Jan/23

$$R=37$$$$s=\frac{37+37+24}{2}=49$$$$Area\left(MGI\right)=\sqrt{49{(49-37)}^2(49-24)}=420$$$$GC=\sqrt{{37}^2-\frac{{23}^2\cdot 2}{4}}-\frac{23\sqrt{2}}{2}\approx 17$$$$2Area\left(GCH\right)=2\left(\frac{17\cdot \frac{23\sqrt{2}}{2}}{2}\right)=\frac{391\sqrt{2}}{2}$$$$420+\frac{391\sqrt{2}}{2}\approx 696u^2$$

Commented by HeferH last updated on 27/Jan/23

Commented by mr W last updated on 27/Jan/23

$$itistoprovethatHC=IC.$$

Commented by HeferH last updated on 27/Jan/23

$$\frac{CA}{24}=\frac{23}{70}\Rightarrow CA=\frac{23\cdot 12}{35}=\frac{276}{35}$$$$\frac{{QQ}^{\prime }}{24}=\frac{47}{70}\Rightarrow {QQ}^{\prime }=\frac{47\cdot 12}{35}=\frac{564}{35}$$$$\left(\frac{276+564}{35}\right)\cdot \frac{1}{2}\cdot 24\cdot \frac{1}{2}+24\cdot 23=696u^2$$

Commented by HeferH last updated on 27/Jan/23

$$yes$$

Answered by mr W last updated on 27/Jan/23

Commented by mr W last updated on 27/Jan/23

$$a=24$$$$b=23$$$$c=?$$$$\sin \alpha =\frac{b}{\sqrt{2}R}=\frac{\sqrt{b^2+c^2}}{2R}$$$$\sqrt{2}b=\sqrt{b^2+c^2}$$$$\Rightarrow b^2=c^2\Rightarrow c=b✓$$$${\left(\sqrt{2}R\right)}^2={(a+c)}^2+b^2=a^2+2b(a+b)$$$$\Rightarrow R=\sqrt{\frac{a^2+2b(a+b)}{2}}$$$$=\sqrt{\frac{{24}^2+2\times 23\times (24+23)}{2}}=37$$$$green=\frac{a}{2}\sqrt{R^2-\frac{a^2}{4}}+\frac{\sqrt{2}b}{2}\sqrt{R^2-\frac{b^2}{2}}-\frac{b^2}{2}$$$$=12\times 58=696$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com