Use the diagram of Circle C below to answer the questions. Assume m

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

sure thing bud

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3boys + 4 girls = 7 students

3 boys to students   true   yes

4 girls to 3 boy   true     yes

3 boys to 7 girls   false   no

4 girls to 7 students   true   yes