Question

Let AB be a line segment with midpoint C. and D be the midpoint of AC Let C1 be the circle with diameter AB. and C2 be the circle with diameter AC Let E be a point on C1 such that EC is perpendicular to AB Let F be a point on C2 such that DF is perpendicular to A B. and E and F is on opposite sides of AB Then the value od angle FEC is ??​

Answer 1

∠FEC = Tan⁻(1/3)

Step-by-step explanation:

Lets Join EF which intersect CD  at  M

now in Δ MDF & ΔMCE

∠DMF = ∠CME  ( opposite angles)

∠MDF  = ∠MCE = 90°

=>  Δ MDF ≈ ΔMCE

=> MD /MC  = DF/CE

DF = Radius of Circle C2

CE = Radius of Circle C1

=> DF / CE = 1/2

=> MD /MC = 1/2

=> MC = 2MD

CD = Radius of Circle C2 = MC + MD

=> Radius of Circle C2  = MC + MC/2

=> Radius of Circle C1 / 2 =  3MC/2

=> Radius of Circle C1 = 3MC

=> MC / Radius of Circle C1 = 1/3

=> MC/ CE = 1/3

=> Tan ∠MEC = 1/3

=> Tan ∠FEC = 1/3   as M lies on FE

=> ∠FEC = Tan⁻(1/3)

Answer 2

Answer:

Hi friend,

I'm giving the sine value of angle GEC.

Hope it Helps!

Step-by-step explanation:

As given in the images.