Question

AB is a diameter of the circle with center O .if AC and BD are perpendicular on a line Pq and BD meets the circle at E then prove that AC = ED

Answer 1

look close, angle BEA=90 deg.

Hence, angle CAE=90 deg
making quad ACDE a rectangle. By a rectangle's property,AC=ED

Answer 2

Diameter of the circle = AB (Given)

Centre of the circle = O (Given)

AC ⊥ BD on line = PQ (Given)

Thus,

By property of angles,  

∠AEB =   90°

Similarly,

All the angles in the quadrilateral AEDC will be =  90°

Therefore, AEDC is a rectangle

Since AEDC is a rectangle then AC = ED as opposite sides of rectangle are always equal.