ANSWER:
EH = 14
CH = √277
The value of EH is 14 and the value of CH is √277.
STEP-BY-STEP EXPLANATION:
As H is the circumcenter of triangle BCD, it must be the half-way point between point E and point D or line ED. This means EH is equivalent to HD.
THEREFORE:
EH = HD
EH = 14
Angle CEH is a right angle.
Angle CEH = 90°
Therefore, triangle CEH is a right-angle triangle. This means that we can use Pythagoras' Theroem to obtain the value of CH.
Pythagoras' Theroem is as follows:
a^2 + b^2 = c^2
Where c = hypotenuse of right-angle triangle
Where a and b = other two sides of right-angle triangle.
From this, we will substitute the values from the problem and that we have already established into the formula to obtain the value of CH.
a^2 + b^2 = c^2
a = CE = BC ÷ 2 = 18 ÷ 2 = 9
b = EH = 14
c = CH = ?
THEREFORE:
( 9 )^2 + ( 14 )^2 = ( CH )^2
( CH )^2 = 81 + 196
( CH )^2 = 277
CH = √277
