Question

Simple Math Puzzle on triangles.

ABCD is a square. Green circle's radius = 2 cm. Blue circle has a radius = 4 cm.
Find the length "a" of the edge of the square.

Use the formulas related to triangles.

Answer 1

Hey there,

PF = KO = KF = 4cm
 BP = BT ; CK = CT =[ Tangents to a circle from common point ]

Perimeter [ BFC ] = BP + PF + KF + KC + BC
Perimeter [ BFC ] = ( BT + CT ) + PF + KF + BC
Perimeter [ BFC ] = a + a + 4 + 4
Perimeter [ BFC ] = 2a + 8

16[ 2a + 8 ]/2 + 16 = a²
16a + 64 + 16 = a²
a² - 16a - 80 = 0
a = 20, -4

Hence, a = 20 is the solution.

Hope this helps!

Answer 2

ANSWER IS IN THE IMAGE