Question

Help. diagram shows a circle PQRS with centre O and radius 10cm. PQTS is a sector of a circle with centre P that INSCRIBED in the circle PQRS.
Calculate the length of arc QTS.

Answer 1

first calculate angle QOS
radius = 10 cm
arc length = angle QOS (in Radians) * radius

Answer 2

If i do it like that. I ll get the length of arc QRS??

Answer 3

i think you can get arc length QTS
radius = 20 cm
angle QPS = pi/3
arc length = angle QPS (in Radians) * radius
try to solve like this

Answer 4

@uzumakhi, is partially correct.

arc length equals to the product of the central angle in radians and the radius of the circle.

Answer 5

QOP AND OSP SIMILAR

Answer 6

when i see diagram carefully i come to know that arc QTS is arc of circle with center P therefore its angle is 60 degree and radius 20 cm

Answer 7

i am not sure about its radius

Answer 8

\[PQ = 2r \sin(\frac{ \theta }{ 2 }) \]
where theta is 120 degree

Answer 9

10 x radians (120 degrees)

Answer 10

Looking at POS, then radius PS is 2* 10 cos 30 = 10 sqrt 3 ?

Answer 11

PQS may not be equilateral triangle

Answer 12

radius = 17.3 cm
angle QPS = 60 degree
arc length = angle QPS (in Radians) * radius
try to solve like this

Answer 13

@uzumaki How do u know that the radius is 17.3 ?

Answer 14

10 sqrt 3

Answer 15

\(\triangle OSP \cong \triangle OQP\) by SSS

Answer 16

PQ=2rsin(θ/2)

Answer 17

60/360 = QS/(2pi 10 sqrt 3)

Answer 18

this PQ is Radius

Answer 19

PS = 20 cos 30

Answer 20

length of QTS = \(\frac{rad(60 degrees)}{20 cos 30}\)

Answer 21

THANK YOU . I get it now. So the answer is 18.14 cm. is it?

Answer 22

yes you are right

Answer 23

i have th eformula wrong there,

length of QTS = \(rad(60 degrees) \times 20 cos 30 \) = 18.14

Answer 24

QTS=18.14CM