A restaurant can seat 100 people. It has booths that seat 4 people and tables that seat 6 people. So far, 5 of the booths are fu
1 answer:
You might be interested in
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
#SPJ1
In the given diagram, the measure of ∠3 will be 105°.
In the given diagram, ∠3 and ∠6 are consecutive interior angles.
<h3>How to form supplementary angles by transversal?</h3>If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles formed are supplementary.
That is,
∠3 + ∠6 = 180°
From the given information,
∠6 = 75°
Then,
∠3 + 75° = 180°
∠3 = 180° - 75°
∠3 = 105°
Hence, the measure of ∠3 will be 105°.
Learn more about the measures of angles here: brainly.com/question/2883630
#SPJ1
