Answer:
17) Length of arc QPT = 20.9 inches
18) Length of arc QR = 12.6 feet
19) Length of arc PQR = 39.3 meters
20) x = 161°
21) x = 123°
22) x = 24 units
23) EB = 4 units
24) EB = 14 units
Step-by-step explanation:
∵ The length of any arc = Ф/360 × 2πr
where Ф is the central angle subtended by this arc
17) ∵ m∠RZQ = 60° ⇒ central angle
∵ m∠QZP = 90° ⇒ centeral angle
∵ m∠RZT = 180° ⇒ Z ∈ TR
∴ m∠TZP = 180 - 90 - 60 = 30°
∴ m∠QZT = 90 + 30 = 120° ⇒ central angle
∵ ∠QZT subtended by arc QPT
∵ m∠QZT = 120 , r = 10 inches
∴ Length arc QPT = 120/360 × 2π × 10 = 20.9 inches
18) ∵ m∠QZR = 60° ⇒ central angle subtended by arc QR
∵ r = 12 feet
∴ The length of arc QR = 60/360 × 2π × 12 = 12.6 feet
19) ∵ m∠PZR = 60° + 90° = 150°⇒ central angle subtended
by arc PQR
∵ r = 15 meters
∴ The length of arc PQR = 150/360 × 2π × 15 = 39.3 meters
20) ∵ SU = ST
∴ Measure of arc SU = measure of arc ST
∵ The measure of the circle is 360°
∵ Measure of arc UT = 38°
∴ x = (360 - 38) ÷ 2 = 161°
21) ∵ AB = AC
∴ Measure of arc AB = measure of arc AC
∵ The measure of the circle is 360°
∵ Measure of arc BC = 114°
∴ x = (360 - 114) ÷ 2 = 123°
22) ∵ The two arcs are equal
∴ Their chords are equal in length
∴ 2x - 12 = 36 ⇒ 2x = 36 + 12 ⇒ 2x = 48
∴ x = 24
23) In circle A
∵ AB is a radius and CD is a chord
∵ AB ⊥ CD
∴ AB bisects CD at point E
∵ AB = 20 , CD = 24
∴ CE = 24/2 = 12
In ΔAEC
∵ m∠ AEC = 90
∵ AC = 20 ⇒ radius
∵ AE = √[(AC)² - (CE)²] ⇒ Pythagoras theorem
∴ AE = √(20² - 12²) = 16
∵ AB = 20 ⇒ radius
∴ EB = 20 - 16 = 4
24) In circle A
∵ AB is a radius and CD is a chord
∵ AB ⊥ CD
∴ AB bisects CD at point E
∵ AB = 35 , CD = 56
∴ CE = 56/2 = 28
In ΔAEC
∵ m∠ AEC = 90
∵ AC = 35 ⇒ radius
∵ AE = √[(AC)² - (CE)²] ⇒ Pythagoras theorem
∴ AE = √(35² - 28²) = 21
∵ AB = 35 ⇒ radius
∴ EB = 35 - 21 = 14
