MathDB

A triangle

ABC

is given. Let

C'

and

C'_{a}

be the touching points of sideline

AB

with the incircle and with the excircle touching the side

BC

. Points

C'_{b}

C'_{c}

A'

A'_{a}

A'_{b}

A'_{c}

B'

B'_{a}

B'_{b}

B'_{c}

are defined similarly. Consider the lengths of

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altitudes of triangles

A'B'C'

A'_{a}B'_{a}C'_{a}

A'_{b}B'_{b}C'_{b}

A'_{c}B'_{c}C'_{c}

. (a) (8-9) Find the maximal number of different lengths. (b) (10-11) Find all possible numbers of different lengths.

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