Could you please help me out In this geo problem for finding more elegant soln , although I have already solved it but its kind of too long , ABCD is a cyclic quadrilateral with side lengths as follows. AB = 6 cm, BC = 12cm , CD = 3 cm and DA = 6 cm.let the intersection of AB and CD be "E" and intersection of CB and AD be "F". Find the length of EF
you can prove that triangle EAD is similar to triangle ECB and triangle FDC is similar to triangle FBA. Then you can calculate that EA=4 and ED =5, FD=10 and FC=8. Then you know that triangle EDF is similar to triangle ADC, therefore, AC// EF. AB^2+BC^2-2AB*BC*cos ABC=AD^2+DC^2+2AD*DC*cos ABC. So cos ABC=3/4. Then AC=6sqrt2. So EF=10sqrt2.
Not sure if my method is the best solution. And if you want I can open a new playlist as problems from audience to solve it publicly. No pressure, only if you are willing to.
My soln was kind very similar to yours Soln. •By power of point of "E" ( EA)(EB)=(ED)(EC).......(1) • Notice that CA is angle bisector of angle《DCB in triangle 🔺️ ECB (ED+DC)/(BC) = (EA)/(AB)...(2) From eqn 1 and 2 We get ED=5 ; EA=4 Apply meneluas theorem In 🔺️ EBC and with line A-D-F We get CF=8 Using cosine rule in triangle 🔺️ AED We get Cos(《EAD) = -9/16 ==> Cos(《ECF) = 9/16 To finish use cosine rule in triangle FEC
And regarding to a new playlist for your youtube family and specially for me I would highly encourage your effort toward your hardships for us And at last I want you to start a new separate playlist on geometry, where we can send you problem's or doubt so that you can explain them in your video's. & ❤Thanks for your response
Excuse me could you please help me If PN is the perpendicular from any point P to the radical axis of two circles the centers of which are A, B, and PQ, PR are the tangents from P to the circles, then PQ Power of 2 - PR Power of 2 = 2 PN ΑΒ. CONSTRUCTION: Draw PM ꓕ AB, and join PA, AQ, PB, BR
I’m not sure if I understand the problem set but it looks like there’s no definition of point N. We only know PN is perpendicular to radical axis. But how to define where N is?
Could you please help me out
In this geo problem for finding more elegant soln , although I have already solved it but its kind of too long ,
ABCD is a cyclic quadrilateral with side lengths as follows. AB = 6 cm, BC = 12cm , CD = 3 cm and DA = 6 cm.let the intersection of AB and CD be "E" and intersection of CB and AD be "F". Find the length of EF
you can prove that triangle EAD is similar to triangle ECB and triangle FDC is similar to triangle FBA. Then you can calculate that EA=4 and ED =5, FD=10 and FC=8. Then you know that triangle EDF is similar to triangle ADC, therefore, AC// EF. AB^2+BC^2-2AB*BC*cos ABC=AD^2+DC^2+2AD*DC*cos ABC. So cos ABC=3/4. Then AC=6sqrt2. So EF=10sqrt2.
Not sure if my method is the best solution. And if you want I can open a new playlist as problems from audience to solve it publicly. No pressure, only if you are willing to.
My soln was kind very similar to yours
Soln.
•By power of point of "E"
( EA)(EB)=(ED)(EC).......(1)
• Notice that CA is angle bisector of angle《DCB in triangle 🔺️ ECB
(ED+DC)/(BC) = (EA)/(AB)...(2)
From eqn 1 and 2
We get ED=5 ; EA=4
Apply meneluas theorem In 🔺️ EBC and with line A-D-F
We get CF=8
Using cosine rule in triangle 🔺️ AED We get Cos(《EAD) = -9/16
==> Cos(《ECF) = 9/16
To finish use cosine rule in triangle FEC
And regarding to a new playlist for your youtube family and specially for me I would highly encourage your effort toward your hardships for us
And at last I want you to start a new separate playlist on geometry, where we can send you problem's or doubt so that you can explain them in your video's.
&
❤Thanks for your response
Excuse me could you please help me
If PN is the perpendicular from any point P to the radical axis of two circles the centers of which are A, B, and PQ, PR are the tangents from P to the circles, then PQ Power of 2 - PR Power of 2 = 2 PN ΑΒ.
CONSTRUCTION: Draw PM ꓕ AB, and join PA, AQ, PB, BR
I’m not sure if I understand the problem set but it looks like there’s no definition of point N. We only know PN is perpendicular to radical axis. But how to define where N is?
@ Point N is from drawing a horizontal line, drawn to point P. We can determine the length, but anyway I still can't solve this geometry problem😭