Question

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

Answer 1

Answer:

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.

• Length of RS = 6 ; Length of AS = RS - AR = 6-x

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

• Length of ST = 9 ; Length of TB = ST - SB = 9 - (6-x) = 3+x

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

• Length of TU = 7 ; Length of UC = TU - TC = 7 - (3+x) = 4-x

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

• Length of UV = 15 ; Length of VD = UV - UD = 15 - (4-x) = 11+x

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

• Length of VR = 14 ; Length of RE = VR - VE = 14 - (11+x) = 3-x

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

RA = RE

x = 3 - x

2x = 3

x = $\frac{3}{2}$

x = 1.5