Use analytic geometry to prove that an angle inscribed in a semicircle is a right angle.
G Guest Guest Nov 6, 2005 #1 Use analytic geometry to prove that an angle inscribed in a semicircle is a right angle.
pka Elite Member Joined Jan 29, 2005 Messages 11,995 Nov 6, 2005 #2 y=r2−x2\displaystyle y = \sqrt {r^2 - x^2 }y=r2−x2 is a semi circle centered at the origin with radius r. If (p,q) is point on the semi circle then p2+q2=r2\displaystyle p^2 + q^2 = r^2p2+q2=r2 Show that the line through the (p,q) and (−r,0) is perpendicular to the line through (p,q) and (r,0).
y=r2−x2\displaystyle y = \sqrt {r^2 - x^2 }y=r2−x2 is a semi circle centered at the origin with radius r. If (p,q) is point on the semi circle then p2+q2=r2\displaystyle p^2 + q^2 = r^2p2+q2=r2 Show that the line through the (p,q) and (−r,0) is perpendicular to the line through (p,q) and (r,0).
