This question was uploaded on 13/09/21 on social media accounts.
Two Squares bases are at 120° and an equilateral triangle is drawn with one side on two ends of the square. The distance between one vertex of the triangle and the common vertice is 60. Find the sum of the area of both squares.
Solution:
Method 1:
Triangle OPQ is equilateral triangle:
OP = OQ = PQ = 60
⇒ 3x = 60
⇒ x = 20
Area:
A = 5x² = 2000
Explanations:
The bottom angle is 60:
Angle BOQ = Angle APO
By this Angle APB = Angle POQ = 60
Triangle POQ is equilateral triangle:
Angle POQ = 60, OP = OQ,
⇒ Angle OPQ = Angle OQP
This puzzle was made on the occasion of 2000 followers.
Method 2:
By using "Ptolemy Theorem":
(a)(x) + (a)(2x) = (a)(60)
⇒ x + 2x = 60
⇒ x = 20
⇒ Area = 5x² = 2000
Explanation:
How circle touches 4 points:
Quadrilateral drawn on that 4 points is a cyclic quadrilateral (Sum of measure of opposite angles is 180)
Due to the same reason, Ptolemy Theorem can be applied here.
Puzzle related to Geometry, Square, Triangle, Area.
