What is the length of the shorter of the two chords shown?

the length of the shorter chord is units

answer: the length of the shorter chord is 13 units i.e. qs.

step-by-step explanation:

since we have given that

there is two chords i.e. qs and rt.

as we know the formula :

length of chord qs is given by

length of chord tr is given by

so, the length of the shorter chord is 13 units i.e. qs.

Using the intersecting chord theorem, we can say

qa*as = ta*ar

plug in the given segment expression lengths. then solve for x
qa*as = ta*ar
9*4x = 12*(x+2)
36x = 12x+24
36x-12x = 24
24x = 24
24x/24 = 24/24
x = 1

since x = 1, we can use this to find the missing segment lengths
as = 4*x = 4*1 = 4
ar = x+2 = 1+2 = 3

therefore, the two chords
tr = ta+ar = 12+3 = 15
qs = qa+as = 9+4 = 13

the shorter chord is qs
the length of the shorter chord is 13 units.