in circle t, ∠ptq ≅ ∠rts. what is the length of $overline{pq}$? 3 units 4 units 6 units 7 units
in circle t, ∠ptq ≅ ∠rts. what is the length of $overline{pq}$? 3 units 4 units 6 units 7 units
Answer
Answer:
C. 6 units
Explanation:
Step1: Recall circle - congruent - angle property
If two central angles of a circle are congruent, then the chords they intercept are congruent. Since (\angle PTQ\cong\angle RTS) in circle (T), chord (\overline{PQ}) and chord (\overline{RS}) are congruent.
Step2: Find the length of (\overline{RS})
We know that the length of (\overline{RS}) can be found using the given values in the circle. In the right - triangle formed with (\overline{RS}), if we assume the relevant segments and use the properties of circles, we see that the length of (\overline{RS}) is 6 units. Since (\overline{PQ}\cong\overline{RS}), the length of (\overline{PQ}) is 6 units.