Question

In circle P, diameter QS measures 20 centimeters. Circle P is shown. Line segment Q S is a diameter. Line segment R P is a radius. Angle R P S is 123 degrees. What is the approximate length of arc QR? Round to the nearest tenth of a centimeter. 9.9 centimeters 19.9 centimeters 21.5 centimeters 43.0 centimeters

Answer 1

Answer:

Length of arc QR is $\approx$ 9.9 cm

Step-by-step explanation:

Given that circle P, i.e. center is point P.

QS is diameter with length 20 cm.

Given that RP is the radius with

$\angle RPS = 123^\circ$

To find length of arc QR = ?

Solution:

Arc QR subtends the $\angle QPR$ on center P.

So, we need to find the angle $\angle QPR$ to find the length of arc QR.

QS is the diameter so $\angle QPS = 180^\circ$

$\angle QPS = 180^\circ = \angle QPR +\angle RPS\\\Rightarrow 180^\circ = \angle QPR +123^\circ\\\Rightarrow \angle QPR = 57^\circ$

Converting in radians,

$\angle QPR = 57^\circ \times \dfrac{\pi}{180} = 0.99\ radians$

Using the formula for length of arc:

$l = \theta \times R$

Where $\theta$ is the angle subtended by the arc on center.

R is the radius of circle.

Here,

$\theta = 0.99\ radians\\R = 10\ cm$

$l = 0.99 \times 10\\l = 9.9\ cm$

Length of arc QR is $\approx$ 9.9 cm

Answer 2

Answer:

9.9 cm

Step-by-step explanation: