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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

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