It is given that d is the midpoint of ab and e is the midpoint of ac. to prove that de is half the length of bc, the distance formula, d = , can be used to determine the lengths of the two segments. the length of bc can be determined with the equation bc = , which simplifies to 2a. the length of de can be determined with the equation de = , which simplifies to therefore, bc is twice de, and de is half bc.

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step-by-step explanation:

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.