Let ABC be a right triangle with right angle at C. Let D and E be points on AB with D between A and E DE 8
mo
such that CD and CE trisect C. If
then tan B can be written as where m and n are
BE 15
n
relatively prime positive integers, and plis a positive integer not divisible by the square of any prime. Find
m+n + p.

the answer is c. 23/3

6mm^3 or .6cm^3

      216

      /   \

  36     6

  /   \     /

6     6   6

factor trees are nice.

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.