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4 years ago

I dont understand question 3

Mathematics

1 answer:

MA_775_DIABLO [31]4 years ago

6 0

Hello from MrBillDoesMath!

Answer:

col 1: 60

col 2: 60

col 3: 120

col 4: 120

Discussion:

Two lines intersect in two pairs of vertical angles and pairs of vertical angles are equal. Trial and error showed these values shroud do the trick:

col 1: 60

col 2: 60

col 3: 120

col 4: 120

Note the vertical angles: (col 1,col 2) and (col 3, col 4). Also col 1+ col2 + col 3 + col 4 = 360, which is the number of degrees spanned by a line.

Thank you,

MrB

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4 years ago

Two circles with different radii have chords AB and CD, such that AB is congruent to CD. Are the arcs intersected by these chord

emmainna [20.7K]

The arcs intersected by these chords are not congruent.

Given that two circles with different radii have chords AB and CD, such that AB is congruent to CD.

Let r₁ and r₂ be the radii of two different circles with centers O and O' respectively.

Assuming that the each of the ∠АОВ and ∠CO'D is less than or equal to π.

Then, we have isosceles triangle AOB and CO'D such that,

AO = OB = r₁,

CO' = O'D = r₂,

Let us assume that r₁< r₂;

We can see that arc(AB) intersected by AB is greater than arc(CD), intersected by the chord CD;

arc(AB) > arc(CD) .......(1)

Indeed,

arc(AB) = r₁ angle (AOB)

arc(CD) = r₂ angle (CO'D)

So, we have to prove that ;

∠AOB >∠CO'D ......(2)

Since each angle is less than or equal to π, and so

∠AOB/2 and ∠CO'D/2 is less than or equal to π

it suffices to show that :

tan(AOB/2) >tan(CO'D/2) ......(3)

From triangle AOB :

tan(AOB/2) = AB/(2*r₁)

tan(CO'D/2) = CD/(2*r₂)

Since AB = CD and r₁ < r₂ (As obtained from the result of (3) ), therefore, arc(AB) > arc(CD).

Hence, for two circles with different radii have chords AB and CD, such that AB is congruent to CD but the arcs intersected by these chords are not congruent.

Learn more about congruent from here brainly.com/question/1675117

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