Question

point s lies in the exterior of a circle with centre p and radius 33 cm . a tangent from s touches the circle t and st =56 cm . find the distance of s from p.​

Answer 1

If the tangent ST = 56 cm and radius is 33 cm then the distance of s from p is 65 cm.

Step-by-step explanation:

It is given,

ST is a tangent to the circle touching the circle at point T and ST = 56 cm

The radius of the circle, PT = 33 cm

Since a tangent to a circle is perpendicular to the radius through the point of contact, therefore,  

∠PTS = 90°

Let the distance of s from p be denoted as “SP”.

Now referring to the figure attached below, and by using Pythagoras theorem, in ∆ PTS, we get

PS² = PT² + ST²

⇒ PS² = 33² + 56² ….. [substituting the given values]

⇒ PS = √[33² + 56²]

⇒ PS = √[1089 + 3136]

⇒ PS = √[4225]

⇒ PS = 65 cm

Thus, the distance of s from p is 65 cm.

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Answer 2

GIVEN: ST Is a tangent to the circle touching the circle at point T and ST = 56cm

any tangent to the circle is always form right angle so,

PTS = 90°

Let the distance of S from P = SP

NOW BY PYTHAGORAS THEOREM

in triangle PTS we get ;

PS² = PT² + ST²

= PS² = 33² + 56²

= PS = √1089 + 3136

= PS = √4225

= PS = 65cm

THUS WE GET THE DISTANCE BETWEEN P AND S i.e; 65cm.

hope you get it ....!

thankyou.