Given a sentence in English language, translate the sentence to Tagalog language keeping the meaning of the original sentence intact.

English sentence: The point M is the midpoint of the arc BC on the circle c. Thus, the two chords BM and CM of the circle c have equal length. Hence, the chordal angles of these two chords must also be equal; in other words, we have &lt; BAM = &lt; CAM. Hence, the point M lies on the angle bisector of the angle BAC. Similarly, the point N lies on the angle bisector of the angle BAD. But, of course, the angle bisector of the angle BAD is the exterior angle bisector of the angle BAC; hence, since the interior and the exterior angle bisector of an angle are always perpendicular to each other, the angle bisector of the angle BAC and the angle bisector of the angle BAD are perpendicular to each other. Hence, &lt; MAN = 90°.
Ang point M ay ang midpoint ng Arc BC sa circle c. Kaya, ang dalawang Chords BM at CM ng c bilog ay may pantay na haba. Kaya, ang chordal angles ng mga dalawang Chords ay dapat pantay-pantay, sa ibang salita, mayroon kaming &lt; BAM = &lt; CAM. Kaya, ang point M kasinungalingan sa anggulo panggitnang guhit ng anggulo BAC.

English sentence: Mirsky's talent for teaching was clearly related to his gifts as a writer and is described in as follows:
Mirsky's talento para sa pagtuturo ay malinaw na may kaugnayan sa kanyang mga regalo bilang isang writer at ito ay inilarawan sa mga sumusunod:

English sentence: He undertook research in complex analysis supervised by John McDonald and he was awarded a Ph.D. in December 1934 for his thesis Some results in the theory of Schlicht functions.

Siya undertook pananaliksik sa mga komplikadong pagtatasa supervised by John McDonald at siya ay iginawad ng isang Ph.D. sa Disyembre 1934 para sa kanyang tesis Ang ilang mga resulta sa teorya ng Schlicht function.