Answer:
a) CE = 9
b) Perimeter = 36.1
Explanation:
a)
Using the property of chords in a circle, we have that:
DE * BE = AE * CE
As the diameter is perpendicular to the chord, the diameter cuts the chord in half, so BE = DE = BD/2 = 6
So we have that:
6 * 6 = 4 * CE
4 * CE = 36
CE = 9
b)
As the triangle BCE is congruent to the triangle DCE (using side-angle-side case), we have that BC = CD, and we can find them using Pythagoras' theorem in the triangle BCE:
BC^2 = DE^2 + EC^2
BC^2 = 6^2 = 9^2
BC^2 = 36 + 81 = 117
BC = 10.8167
As the triangle BAE is congruent to the triangle DAE (using side-angle-side case), we have that AB = AD, and we can find them using Pythagoras' theorem in the triangle BAE:
AB^2 = AE^2 + BE^2
AB^2 = 4^2 = 6^2
AB^2 = 16 + 36 = 52
AB = 7.2111
So the perimeter of ABCD is:
10.8167 + 10.8167 + 7.2111 + 7.2111 = 36.0556
Rounding to the nearest tenth, the perimeter is 36.1