There are some theories based on Ramayana. According to "All India Roundup" and "Speaking Tree", Ramayana by Valmiki has mention of such triangle.
Ramayana features the story of a Demoness Simhika (Chhayagrahi) who used to reside in the Indian ocean and was awarded the boon of grasping any object or being towards her, however, powerful it might be, by Lord Brahma. She was famously known Chhayagrahi because she had the mystical power of pulling any object/entity with a glance at the shadow of the object. She had a huge body and was capable of swallowing bigger objects that she can easily pull towards her. Due to this, no one dared to travel passing nearby her.
Thus, when Hanuman flew over the ocean in search of Sita Maa, he felt his speed slowing down, feeling powerless, under immense invisible pressure. Later on seeing here and there, up and down, Lord Hanuman sees floating demoness pulling his shadow towards her. She tried to eat Hanuman, however, Hanuman killed her by decreasing the size of his massive body and entering her mouth later destroying her internal organs.
It has been said that fearing from the act of Lord Hanuman, daughter of demon Simhika ran away from the Hindu Maha Samudra (Indian Ocean) to some mysterious place, which apparently is the Bermuda Triangle.
According to epic, King Ravana, with his dhyan, penance, austerity towards Lord Shiva, got several boons which added to his strength making him almost invincible. The secret to Ravan’s massive strength was due to his blessings of Lord Shiva. He was also gifted with a gem which helped in the regeneration of nectar at his navel, dictated that he could not be vanquished for as long as it lasted. This made him amar (immortal) and no one could kill him unless the gem be taken back from him so that nectar from the navel could be soaked.
During the war between Ram and Ravan, Lord Shiva, who knew that Mandodari (devout wife of Ravan and also a devotee of Lord Shiva) was aware of the place where Ravan had hidden that mani (gem), took the appearance of a Sage and asked for the ‘mani’ as Dakshina from Mandodari. No devotee of Lord Shiva could ever say no to the Sage for Dakshina. Mandodari knew that secret of mani is only known to Lord Shiva, Ravan and her. She understood that Sage is no one but Lord Shiva himself. She came to know that the Ramlila is about to end with the death of Ravan and gave the mani to Lord Shiva as Dakshina.
After this incident, the demon king of Sri-Lanka, Ravan was killed by Bhagwan Shree Ram. Lord Rama killed Ravana by firing the ‘Arrow of Brahma’ at his navel (This arrow of Brahma was given to Rama by Sage Agastya). This made Ravan lifeless and he fell down to the ground, the nectar of immortality soaked from his navel and this led to his death.
After the death of Ravana, it became imperative that the gem be placed in a zone that absorbs its energy and uncontrollable power. The gem was so powerful that its presence could impact future generations too. Lord Hanuman was given the task of placing the mani to the depth (core) of the ocean bed, very deep so that its impact could be minimized and diluted. The mani was apparently placed in the deepest core of Ocean of that time which today is known as Bermuda Triangle.
This makes us believe that the immense grabbing power of mani is the probably the main reason that pulls down the objects flowing or floating nearby or above Bermuda Triangle.