In figure 3.93, m(arc WY) = 44°, m(arc ZX) = 68°, then (1) Find the measure of ∠ZTX. (2) If WT = 4.8, TX = 8.0, YT = 6.4, find TZ. (3) If WX = 25, YT = 8, YZ = 26, find WT.

In figure 3.93, m(arc WY) = \(44^\circ\), m(arc ZX) = \(68^\circ\), then

(1) Find the measure of \(\angle ZTX\).

(2) If WT = 4.8, TX = 8.0, YT = 6.4, find TZ.

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

Figure: Chords WX and YZ intersect at T inside the circle.

Doubtly Asked 24 Oct 2026 Save WhatsApp Report

1 answer

Answer: (1) \(56^\circ\) (2) TZ = 6 (3) WT = 16 or 9

(1) For chords intersecting inside a circle,

\[\angle ZTX = \frac{1}{2}[m(\text{arc ZX}) + m(\text{arc WY})]\] \[= \frac{1}{2}(68^\circ + 44^\circ) = 56^\circ\]

(2) \(WT \times TX = YT \times TZ\):

\[4.8 \times 8 = 6.4 \times TZ\] \[TZ = \frac{38.4}{6.4} = 6\]

(3) TZ = YZ − YT = 26 − 8 = 18. Let WT = x, then TX = 25 − x.

\[x(25 - x) = 8 \times 18 = 144\] \[x^2 - 25x + 144 = 0\] \[(x - 16)(x - 9) = 0\]

WT = 16 or WT = 9.

Doubtly AI · 24 Oct 2026 AI-verified · Oct 2026 Report

Was this answer helpful?