A problem of quadratic term theorem Known xy

A problem of quadratic term theorem Known xy

From tr + 1 = C7 (R) x ^ (7-r) y ^ R, it is obtained that:
T3=C7(2)x^5y^2
T4=C7(3)x^4y^3
The third is not greater than the fourth
That is T3 ≤ T4
C7(2)x^5y^2≤C7(3)x^4y^3
It is reduced to 3x ≤ 5Y
Known XY

Prove the theorem of tangent angle of string,
 

∵∠ CDA is the circumference angle
∴∠CDA=90º
∵ AP is the tangent of a circle
∴∠CAP=90º
∵∠1+∠CAD=180º-∠CDA=90º;
∠2+∠CAD=90º;
∴∠1=∠2.
I hope I can help you!

Proof of Ptolemy's theorem

As shown in the figure, if the quadrilateral ABCD is inscribed in the circle O, then AB * CD + ad * BC = AC * BD
prove:
Make ∠ BAE = ∠ CAD and hand over BD to point E
∵∠ABE=∠ACD,∠BAE=∠CAD
∴△ABE∽△ACD
∴AB/AC=BE/CD
∴AB*CD=AC*BE
∵∠BAC=∠EAD,∠ACB=∠ADE
∴△ABC∽△AED
∴BC/DE=AC/AD
∴BC*AD=AC*DE
∴AB*CD+BC*AD=AC*BE+AC*DE=AC（BE+DE）=AC*BD