analytic geometry

[Guest]

Use analytic geometry to prove that an angle inscribed in a semicircle is a right angle.

 

[pka]

\(\displaystyle y = \sqrt {r^2 - x^2 }\) is a semi circle centered at the origin with radius r.

If (p,q) is point on the semi circle then \(\displaystyle p^2 + q^2 = r^2\)

Show that the line through the (p,q) and (−r,0) is perpendicular to the line through (p,q) and (r,0).

 

[Guest]

Thanks alot your your great response.