# The midpoint perpendicular to the AC side of the ABC triangle intersects the AB side at point T.

The midpoint perpendicular to the AC side of the ABC triangle intersects the AB side at point T. Calculate the degree measure of the ACT angle if you know that the angle BAC = 30 degrees.

Consider the triangle TAS. In a triangle, the height of HT, coinciding with the middle perpendicular to the AC side, that is, AH = HC, and HT is perpendicular to the AC side.

The middle perpendicular means that the perpendicular is restored from the middle of the segment AC, that is, AH = HC.

This means that TH is both the median and the height of the ACT triangle, and this can be in an isosceles triangle. Moreover, AT = TC. The angles at the base of the AC of an isosceles triangle are equal to each other. This means that the angles <TAC = <BAC = <ACT = 30 °.

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