Question-139114

Question Number 139114 by EnterUsername last updated on 22/Apr/21

Commented by mr W last updated on 22/Apr/21

$${i}'{ll}\:{try}\:{to}\:{give}\:{a}\:{proof}\:{when}\:{i}\:{have}\:{time}. \\ $$

Commented by EnterUsername last updated on 22/Apr/21

In ΔABC, origin is the circumcenter, H is the ortho- center and D is the midpoint of the side BC. If P is any point on the circumcircle other than the vertices and T is the midpoint of PH, then the angle between AP and DT is ?

$$\mathrm{In}\:\Delta\mathrm{ABC},\:\mathrm{origin}\:\mathrm{is}\:\mathrm{the}\:\mathrm{circumcenter},\:{H}\:\mathrm{is}\:\mathrm{the}\:\mathrm{ortho}- \\ $$$$\mathrm{center}\:\mathrm{and}\:{D}\:\mathrm{is}\:\mathrm{the}\:\mathrm{midpoint}\:\mathrm{of}\:\mathrm{the}\:\mathrm{side}\:{BC}.\:\mathrm{If}\:{P}\:\mathrm{is} \\ $$$$\mathrm{any}\:\mathrm{point}\:\mathrm{on}\:\mathrm{the}\:\mathrm{circumcircle}\:\mathrm{other}\:\mathrm{than}\:\mathrm{the}\:\mathrm{vertices} \\ $$$$\mathrm{and}\:{T}\:\mathrm{is}\:\mathrm{the}\:\mathrm{midpoint}\:\mathrm{of}\:{PH},\:\mathrm{then}\:\mathrm{the}\:\mathrm{angle}\:\mathrm{between} \\ $$$${AP}\:\mathrm{and}\:{DT}\:\mathrm{is}\:? \\ $$

Commented by mr W last updated on 22/Apr/21