Proving / Properties of Chords with SSS

Question

A. Given: In , radius  bisects chord at point ∙

Prove:  

B. Using , prove that  , given that 

Answer 1

Answer 2

the radius AB= AC=AD = sqr(CE^2 + AE^2)

graph the points and lines on a unit circle with the circle's center at the origin

A(0,0) B(0,1), C(x,y) D(x-y), E (x,0)

sqr(CE^2 + AE^2) = sqr(x^2 + y^2) = sqrt^2 = r = radius = AB

AB is the hypotenuse of a right triangle with sides CE and AE because AB^2 = CE^2 + AE^2

and AB is the hypotenuse of a right triangle with sides DE and AE since AB^2 = DE^2 + AE^2

therefore AB is perpendicular to CD