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

[EX Q]: 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°.
[EX A]: 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.

[EX Q]: English sentence: It’s taken many years, but the world has finally come to a rough understanding of hacker values.
[EX A]: Ito ay kinuha sa maraming mga taon, ngunit ang mundo ay sa wakas dumating sa isang magaspang-unawa ng Hacker halaga.

[EX Q]: English sentence: 111 patients were provided with free eye operations, 108 of which had cataract operations while three underwent three other operations.
[EX A]:
111 pasyente ang nabigyan ng libreng operasyon, 108 ang naoperahan sa katarata habang tatlo ang sumailalim sa iba pang operasyon.