Pentagon rstuv is circumscribed about a circle. what is the value of x if rs = 6, st = 9, tu = 7, uv = 15, and vr = 14?

a. 3
b. 10
c. 4.5
d. 1.5

D. 1.5

Step-by-step explanation:

One basic property you need to keep in mind while solving theses type of questions is as follows :

The length of tangents from an external point on a circle are equal. For simplicity a figure illustrating this property is attached.

Consider S as external point and tangents as SA and SB, so SB=SA=6-x

Consider T as external point and tangents as TB and TC, so TC=TB=3+x

Consider U as external point and tangents as UC and UD, so UD=UC=4-x

Consider V as external point and tangents as VD and VE, so VE=VD=11+x

Now, Consider R as external point and tangents as RA and RE, so

RA = RE

x = 3 - x

2x = 3

x =

x = 1.5

find the magnitude of the trig term  

csc

(

x

)

−

1

by taking the absolute value of the coefficient.

1

find the lower bound of the range.

tap for more

y

=

−

2

find the upper bound of the range.

tap for more

y

=

0

the range is  

y

≤

−

2

or  

y

≥

0

.

(

−

∞

,

−

2

]

∪

[

0

,

∞

)

{

y

|

y

≤

−

2

,

y

≥

0

}

step-by-step explanation: