Question

point A lies in the exterior of a circle with center P and radius 8 cm tangent from A touches the circle at B . if AB = 15cm . find PA​

Answer 1

Answer:

The correct Answer is PA=25cm

Step-by-step explanation:

From the above question,

They have given :

The equation of tangent at point A to the circle with centre P and radius 7 cm is:

(x – h)2 + (y – k)2 = 49

Here, (h, k) is the centre of the circle i.e (h, k) = (P).

Therefore, the equation of tangent at point A to the circle is:

(x – P)2 + (y – P)2 = 49

Given that point A lies in the exterior of a circle with centre P and radius 7 cm, a tangent through A touches the circle at point T.

From the given data, we can calculate the length of PT as follows:

Since, PT is the tangent to the circle and TP is the radius of the circle,

We have PT = 7 cm

Now, we can use the theorem of Pythagoras to calculate the length of PA.

Since, PT and AP are perpendicular to each other,

PA2 = TP2 + AP2

PA2 = 72 + AP2

PA2 = 49 + AP2

AP2 = PA2 - 49

AP2 = PA2 - 49

AP = √(PA2 - 49)

Substituting the value of PT = 7 cm,

We get AP = √(PA2 - 49)

         = √(PA2 - 49)

         = √(252 - 49)

         = √625

         = 25 cm

Hence, the length of PA is 25 cm.

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Answer 2

Answer:

AP^2 = 8^2 - 15^2 = 64 - 225 = -161

Step-by-step explanation:

In this problem we have a circle with center P and radius 8 cm and a point A outside it. A tangent is drawn from A to the circle at B. We need to find the length of PA.

We see that PB is the radius of the circle and AB is the tangent, so they are perpendicular to each other.Hence the triangle PAB is a right triangle. We can use the Pythagorean theorem to find the length of PB:

PB^2 = AB^2 + AP^2

Substituting the given values, we get:

8^2 = 15^2 + PA^2

By simplifying the equation we get:

AP^2 = 8^2 - 15^2 = 64 - 225 = -161

This is not possible because the square of a real number cannot be negative. So there is no real solution for AP.

We can conclude that the values ​​provided are incorrect or that there is an error in the description of the problem.

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