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In the adjoining figure, m(arc WY) = 44° , m(arc ZX) = 68° , then 

i. Find the measure of ∠ZTX. 

ii. If WT = 4.8, TX = 8.0, YT = 6.4, find TZ.

iii. If WX = 25, YT = 8, YZ = 26, find WT.

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i. Chords WX and YZ intersect internally at point T. 

∴ ∠ZTX = 1/2 m(arc WY) + m(arc ZX)] 

= 1/2 (44° + 68°) 

= 1/2 × 112° 

∴ m ∠ZTX = 56° 

ii. WT × TX = YT × TZ [Theorem of internal division of chords] 

∴ 4.8 × 8.0 = 6.4 × TZ 

∴ TZ = (4.8 x 8.0) / 6.4

∴ l(TZ) = 6.0 units 

iii. Let the value of WT be x. [W – T – X] 

WT + TX = WX

∴ x + TX = 25 

∴ TX = 25 – x 

Also, YT + TZ = YZ [Y – T – Z] 

∴ 8 + TZ = 26 

∴ TZ = 26 – 8 = 18 units 

But, WT × TX = YT × TZ [Theorem of internal division of chords] 

∴ x × (25 – x) = 8 × 18 

∴ 25x – x2 = 144 

∴ x2 – 25x + 144 = 0 

∴ (x – 16) (x – 9) = 0 

∴ x = 16 or x = 9 

∴ WT = 16 units or WT = 9 units

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