Perpendicular Chords in a Circle

[Waldlaeufer]

Intersecting chord theorem:
x * 2 = 6 * 4
x = 12

Long side a of red triangle:
a² = 6² + x² = 36 + 144 = 180
a = √180
a/2 = √45

diameter d and radius r of circle:
d² = 2² + 14² = 200
d = √200
r = √50

height h of red triangle:
h² = r² - (a/2)² = 50 - 45 = 5
h = √5

A(red) = a/2 * h = √45 * √5 = √225 = 15 square units

I am going to watch your solution later ... 😊