Ellen has property whose boundary lines form a triangle, as shown in the diagram. her house lies at vertex a and she is going to put a bunkhouse for the ranch hands somewhere along segment bc. she wants the placement to be such that ca/cd=b/a. what must be true about segment ad so that the proportion ca/cd=ba/bd holds

Given that in a ΔABC, Ellen house lies at vertex A and bunkhouse is put somewhere along BC, let it be D.

Please refer the diagram attached.

We are also given that D must be placed such that holds true.

Let us re write the above equation such that CD and BD lie on one side.

That is

Which is nothing but angle bisector theorem.

Hence AD must bisect the angle A then only the given condition will hold true.

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