15 triangles with vertices:

(16,20) (9,24) (8,22)
(16,20) (8,22) (6,21)
(6,21) (16,20) (13,18)
(7,16) (6,21) (13,18)
(12,15) (13,18) (7,16)
(7,16) (12,15) (14,14)
(2,13) (7,16) (14,14)
(10,12) (14,14) (2,13)
(5,10) (2,13) (10,12)
(15,8) (10,12) (5,10)
(3,7) (5,10) (15,8)
(17,6) (15,8) (3,7)
(4,5) (3,7) (17,6)
(19,3) (17,6) (4,5)
(4,5) (19,3) (11,2)