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

English sentence: The name was taken from the name of the town in Luxembourg,
Ang pangalan ay kinuha mula sa mga pangalan ng bayan sa Luxembourg,

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: With the help of the mass media and poll survey firms co-owned by Aquino relatives and allies, bloggers and letter writing brigades paid by public funds in civil and military offices, the Aquino regime has been successful at touting itself as clean and honest on the straight path amidst the rise of corruption in government and as supposedly responsible for economic growth amidst the aggravation of unemployment, poverty and dwindling social services.

Nangangahulugan ito ng mas agresibong paggamit ng dahas at panlilinlang upang tiyakin ang maluwag na pagpasok ng mga dayuhang kapitalista sa anyo ng mga Public-Private Partnership projects sa ating bansa. Mangangahulugan ito ng malawakang pangangamkam ng lupa ng mga magsasaka para bigyang-daan ang mga korporasyon sa agri-business, open-pit mining, konstruksyon ng mga expressway, dambuhalang dam, at iba pang mga katulad na kontrata.