Question

In Fig. , PT and PS are tangents to a circle from a point P such that PT=5 cm and ∠TPS = 60° . Find the length of chord TS.

Answer 1

PS=pt. ( when two tangents met at a point externally then their lenghts are equal)

therefore

angle PTS= angle PST. (angle opp. to equal sides are equal)

now in triangle PTS

angle PTS +angle PST +angle TPS=180

<PTS+<PTS+60=180

2<PTS=180-60

<PTS =60
<PSt =60

therefore all angles are 60 degree it means it is an equilateral triangle

and we know that sides of equilateral triangle are equal

so the cord TS is of 5cm

Answer 2

Answer: The length of chord TS in the figure is 7.07 cm.

To find the length of chord TS in the figure, we need to know the radius of the circle and the length of the tangent PT, and the angle ∠TPS.

With the information given (PT = 5 cm and ∠TPS = 60°), we can use trigonometry to find the length of TS.

Since PT and PS are tangents from the same point P to the circle, they are equal in length.

So, let's call the length of PS also 5 cm.

Next, we can use the angle ∠TPS and the tangent lengths to find the length of TS using the tangent-chord theorem. The theorem states that the tangent from a point to a circle is perpendicular to the radius drawn to the point of tangency. In this case, the radius would be PS, and the length of the radius would be equal to the length of the tangent (5 cm).

So, using the theorem, we can find the length of TS using the Pythagorean theorem:

                          TS^2 = PS^2 + PT^2

                          TS^2 = 5^2 + 5^2

                           TS^2 = 50

                           TS = sqrt(50) = 7.07 cm

Therefore, the length of chord TS in the figure is 7.07 cm.

Learn more about tangents here

https://brainly.in/question/7533031

Learn more about the Pythagorean theorem here

https://brainly.in/question/2829237

#SPJ3