In a trapezoid the lengths of bases are 11 and 18. the lengths of legs are 3 and 7. the extensions of the legs meet at some point. find the length of segments between this point and the vertices of the greater base.

The length of segments between this point and the vertices of greater base are and 18.

Step-by-step explanation:

Let ABCD is the trapezoid, ( shown in below diagram)

In which AB is the greater base and AB = 18 DC= 11, AD= 3 and BC = 7

Let P is the point where The extended legs meet,

So, according to the question, we have to find out : AP and BP

In Δ APB and Δ DPC,

∠ DPC ≅ ∠APB ( reflexive)

∠ PDC ≅ ∠ PAB    ( By alternative interior angle theorem)

And, ∠ PCD ≅ ∠ PBA  ( By alternative interior angle theorem)

Therefore, By AAA similarity postulate,

Let, DP =x

⇒

⇒  33 +11x = 18x

⇒ x = 33/7=

Thus, PD=

But, AP= PD + DA

AP=

Now, let PC =y,

⇒

⇒ 77 + 11y = 18y

⇒ y = 77/7 = 11

Thus, PC= 11

But, PB= PC + CB

PB= 11+7 = 18

the answer would be d.

step-by-step explanation:

move all variables to the left side and all constants to the right side

(x−3)^2+(y−1)^2=16

this is the form of a circle. use this form to determine the center and radius of the circle.

( x − h ) 2 + ( y − k ) 2 = r 2

match the values in this circle to those of the standard form. the variable   r   represents the radius of the circle,   h   represents the x-offset from the origin, and   k   represents the y-offset from origin.

r = 4

h = 3

k = 1

the center of the circle is found at   ( h , k ) .

center:   ( 3 , 1 )

these values represent the important values for graphing and analyzing a circle.

center:   ( 3 , 1 ).

radius:   4

multiplication is multiplication.   it might feel harder depending on what level of math you are in, but generally it will be the same old stuff, while implementing some new concepts and methods of solving work.