Answer:
The length of PQ is 4 units ⇒ 2nd answer
Step-by-step explanation:
In circle T:
- TP , TQ , TR , TS are radii
- PQ and SR are secants
- The measure of arc SR is 66°
- ∠PTQ ≅ ∠RTS
- The length of TR is 3 units
- The length of SR is 4 units
∵ TP , TQ , TR , TS are radii
- The radii of a circle are equal in length
∴ TP = TQ = TR = TS
∵ TR = 3 units
∴ TQ = 3 units
∴ TP = 3 units
∴ TS = 3 units
∵ ∠RTS is a central angle ⇒ its vertex is the center of the circle
∵ ∠RTS is subtended by arc SR
- The measure of the central angle is equal the measure of
its subtended arc
∵ The measure of arc SR = 66°
∴ m∠RTS = 66°
∵ ∠PTQ ≅ ∠RTS
∴ m∠PTQ = 66°
In Δs STR and PTQ
∵ ST = PT ⇒ proved
∵ TR = TQ ⇒ proved
∵ m∠PTQ = m∠RTS
- By using SAS case of congruence theorem
∴ Δ STR ≅ Δ PTQ ⇒ SAS congruence theorem
- As a result of congruence
∴ SR ≅ PQ
∵ SR = 4 units
∴ PQ = 4 units
The length of PQ is 4 units
