Question

(3) If WX = 25, YT = 8,
YZ = 26,find WT​

Answer 1

(3) If WX = 25, YT = 8,  YZ = 26, then WT​ = 16 or WT = 9

Given,

WX = 25, YT = 8 and YZ = 26

Using the theorem of "Internal division of chords", we have,

WT × TX = YT × TZ

WT × (WX - WT) = YT × (YZ - YT)

WT × (25 - WT) = 8 × (26 - 8)

25WT - WT² = 208 - 64

25WT - WT² = 144

WT² - 25WT  + 144 = 0

WT² - 16WT - 9WT  + 144 = 0

WT ( WT - 16 ) - 9 ( WT - 16 ) = 0

( WT - 16 ) ( WT - 9 ) = 0

WT - 16 = 0 , WT - 9 = 0

WT = 16, WT = 9