Prove equal chord of a circle substend equal angle at centre

The Proof for  "Equal chord of a circle subtends equal angle at the Center".

Step-by-step explanation:

Consider a Circle with center as C,

Radius AC ,BC ,DC and EC

Chord AB = Chord CD

To Prove:

"Equal chord of a circle subtends equal angle at center".

i.e ∠ACB = ∠ECD Which are Center angle

Proof:

In  Δ ABC and Δ DEC

Chord AB ≅ Chord DE     .….{Given}

AC ≅ DC                           …..{Radius of Same Circle}

BC ≅ EC                           ….{Radius of Same Circle}

Δ ABC ≅ Δ DEC               ….{By Side-Side-Side Congruence Postulate}

∴∠ACB ≅ ∠ECD  ...{Corresponding Parts of Congruent Triangles are Congruent or CPCTC} ....Proved

i.e Equal chord of a circle subtends equal angle at the Center.

answer: expected value of x = 1.0

step-by-step explanation:

p(x=0) = 0.25

p(x=1) = 0.50

p(x=2) = 0.25

expected value for x = 0×0.25 + 1×0.5 + 2×0.25 = 1.0

the forst and 3rd

step-by-step explanation: