Question: Vaidotas was a son of what ruler of medieval Lithuania who was the Duke of Trakai?

Context paragraphs:
Duchy of Trakai: Duchy of Trakai was a subdivision of the Grand Duchy of Lithuania during the 14th and early 15th centuries.  The Duke of Trakai was an important position held either by the Grand Duke of Lithuania himself or his second-in-command.

Jan Zabrzeziński: Jan Jurjewicz Zabrzeziński or Zaberezhsky (murdered on February 2, 1508) was a noble of Leliwa coat of arms from the Grand Duchy of Lithuania, who achieved the height of his influence during the reign of Alexander I Jagiellon (1492–1506).  He was duke's marshal (1482–1496), regent of Polatsk (1484–1496), castellan of Trakai (1492–1498), voivode of Trakai (1498–1505), and Grand Marshal of Lithuania (1498–1508).  Zabrzeziński was married to Anna, daughter of Jan, elder of Brest and Hrodna.

Kęstutis: Kęstutis (] ; born ca. 1297, died on 3 August or 15 August 1382 in Kreva) was a ruler of medieval Lithuania.  He was the Duke of Trakai and governed the Grand Duchy of Lithuania, 1342–82, together with his brother Algirdas (until 1377), and with his nephew Jogaila (until 1381).  He ruled over the Lithuanians and Ruthenians.

Trakai Peninsula Castle: Trakai Peninsula Castle is one of the castles in Trakai, Lithuania.  It is located on a peninsula between southern Lake Galvė and Lake Luka.  Built around 1350–1377 by Kęstutis, Duke of Trakai, it was an important defensive structure protecting Trakai and Vilnius, capital of the Grand Duchy of Lithuania, against attacks of the Teutonic Knights.  Much of the castle was destroyed in the 17th century.  Remaining walls and towers are preserved and protected by the Trakai Historical National Park.

Petras Jonaitis Mantigirdaitis: Petras Jonaitis Mantigirdaitis (died after 1497) was a prominent noble of the Grand Duchy of Lithuania.  Grandson of Petras Mantigirdaitis, he first appeared in written sources in 1476 and reached his career high in 1490s when he was Voivode of Trakai (1490–97) and Grand Marshal of Lithuania (1491–97).  Chronicler Marcin Bielski described that Alexander Jagiellon was crowned and blessed as the new Grand Duke of Lithuania by the Bishop of Vilnius in 1492.  Then Mantigirdaitis presented Alexander with a naked sword and a reminder that Alexander was elected to be a just ruler.  In 1494, Mantigirdaitis was sent on the diplomatic mission to negotiate peace with the Grand Duchy of Moscow and marriage of Helena of Moscow to Alexander to end the First Muscovite–Lithuanian War.  The Bychowiec Chronicle names him as a Great Hetman who recommended Konstantin Ostrogski, the first official Great Hetman, after his death.  Therefore, it is likely that at some point Mantigirdaitis was the commander of the Lithuanian army.

Lake Galvė: Lake Galvė is a lake in Trakai Lithuania.  It has 21 islands, and one of them houses Trakai Island Castle.  Trakai Peninsula Castle is located on its southern shore.  There are ruins of the little Orthodox church in Bažnytėlė Island.  Trakai was the capital of the Grand Duchy of Lithuania from 1321-1323 before moving to Vilnius.  The lake and most of the other lakes surrounding the castle and city have myths and legends connected to them, of which most contain a tragic love story.  The lakes and castle are therefore also said to be haunted.

Vaidotas: Vaidotas or Wojdat (fl.  1362) was a son of Kęstutis, Grand Duke of Lithuania.  In reliable historical sources he is mentioned only twice: as defender of Kaunas Castle in 1362 and as ruler of Navahrudak.  Due to very limited information, his life is subject to wide-ranging theories by historians.

Algirdas: Algirdas (Belarusian: Альгерд , Russian: Ольгерд , Polish: "Olgierd" ;  1296  – May 1377) was a ruler of medieval Lithuania.  He ruled the Lithuanians and Ruthenians from 1345 to 1377.  With the help of his brother Kęstutis (who defended the western border of the Duchy) he created an empire stretching from the present Baltic states to the Black Sea and to within fifty miles of Moscow.

Trakai: Trakai (   ) (see names section for alternate and historic names) is a historic city and lake resort in Lithuania.  It lies 28 km west of Vilnius, the capital of Lithuania.  Because of its proximity to Vilnius, Trakai is a popular tourist destination.  Trakai is the administrative centre of Trakai district municipality.  The town covers 497.1 km2 of area and, according to 2007 estimates, is inhabited by 5,357 people.  A notable feature of Trakai is that the town was built and preserved by people of different nationalities.  Historically, communities of Karaims, Tatars, Lithuanians, Russians, Jews and Poles lived here.

Trakai Island Castle: Trakai Island Castle (Lithuanian: "Trakų salos pilis" ) is an island castle located in Trakai, Lithuania on an island in Lake Galvė.  The construction of the stone castle was begun in the 14th century by Kęstutis, and around 1409 major works were completed by his son Vytautas the Great, who died in this castle in 1430.  Trakai was one of the main centres of the Grand Duchy of Lithuania and the castle held great strategic importance.

Supporting paragraphs: Vaidotas Kęstutis
Answer: Kęstutis