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Question-22599




Question Number 22599 by ajfour last updated on 20/Oct/17
Commented by ajfour last updated on 20/Oct/17
If P, Q, R be foot of altitudes,  find ((Area( △ABC))/(Area (△PQR))) .
$${If}\:{P},\:{Q},\:{R}\:{be}\:{foot}\:{of}\:{altitudes}, \\ $$$${find}\:\frac{{Area}\left(\:\bigtriangleup{ABC}\right)}{{Area}\:\left(\bigtriangleup{PQR}\right)}\:. \\ $$
Commented by Tinkutara last updated on 20/Oct/17
Can you prove that circumradius of  ΔPQR is half the circumradius of ΔABC?  Also how to find the sides?
$$\mathrm{Can}\:\mathrm{you}\:\mathrm{prove}\:\mathrm{that}\:\mathrm{circumradius}\:\mathrm{of} \\ $$$$\Delta\mathrm{PQR}\:\mathrm{is}\:\mathrm{half}\:\mathrm{the}\:\mathrm{circumradius}\:\mathrm{of}\:\Delta\mathrm{ABC}? \\ $$$$\mathrm{Also}\:\mathrm{how}\:\mathrm{to}\:\mathrm{find}\:\mathrm{the}\:\mathrm{sides}? \\ $$
Commented by ajfour last updated on 20/Oct/17
Yes,  i can. but it is lengthy.
$${Yes},\:\:{i}\:{can}.\:{but}\:{it}\:{is}\:{lengthy}. \\ $$
Commented by Tinkutara last updated on 20/Oct/17
Please can you post that?
$$\mathrm{Please}\:\mathrm{can}\:\mathrm{you}\:\mathrm{post}\:\mathrm{that}? \\ $$
Commented by ajfour last updated on 21/Oct/17
See  Q.22649.
$${See}\:\:{Q}.\mathrm{22649}. \\ $$

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