find the length of CE

ABD is also right angled triangle.

Also BD = DC, and AE = ED .........given.

In ABC,  AB² = AC² - BC² = 25 - BC²

In ABD, AB² = AD² - BD² = AD² - (BC/2)² =45/4 - BC²/4

Hence,

25 - BC² = (45 - BC²)/4

BC = (55/3)

and

AB² = 25 - 55/3 = (75 - 55)/3 = 20/3

AB = (20/3)

ED = AB/2 = (5/3)

In EBC

CE² = ED² + BC²

= 5/3 + 55/3 = 60/3 = 20

CE = 20 = 25 cm.

Regards,

Team,

TopperLearning.