Question

R and t are points on a circle, centre o, with radius 5 cm. Pr and pt are tangents to the circle and angle pot = 78°. A thin rope goes from p to r, around the major arc rt and then from t to p. Calculate the length of the rope.

Answer 1

Given: r = 5 cm

∠POT = 78°

Formula used:

Length of arc = $\frac{2\pi r}{360}$θ

Circumference of circle = $2\pi r$

where r is radius

and θ is central angle

here, ∠POR =∠POT (∵ΔPOR ≅ ΔPOT by RHS congruence condition)

So the length of arc P'R =  $\frac{2\pi * 5 * 78}{360} = 6.81$

since the rope is around the major arc,

the length of major arc = circumference - length of arc P'R

Circumference = $2\pi r =2\pi *5=31.42$

Length of the rope = 31.42-6.81 = 24.61 cm

Answer 2

Answer:

In simple formula,

Step-by-step explanation:

Length of arc =(θ/360)*2*pi*r

= (2*pi*5)*(78/360)=6.81

{Angle POT= Angle POR}

2*pi*5= 31.42

(Bcz it is the major arc so,)

=> 31.42-6.81= 24.61cm