In the figure PT is a tangent to the circle at T. If PA = 4 cm and AB = 5cm then PT =

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

4cm

5cm

6cm

answer is C.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

From the given figure, we can see that OA, OB and OT are the radius of circles. Let us assume that the radius of the circle is r.
Question Image

From the above figure let us consider the triangle OTP right angled at T. Here in triangle OTP, base is PT, altitude is OT and hypotenuse is OP.
Now let us consider the formula Pythagoras Theorem, sum of squares of two sides of a right-angled triangle is equal to square of hypotenuse.
So, using it we get,
Question Image

Now let us consider the chord AB.
Now let us consider the property that any line perpendicular to a chord of the circle from the centre bisects the chord of the circle.
Here AB is a chord and OS is perpendicular to AB. So, from the above property we can say that S is the midpoint of AB.
So, as we have that AB=5cm, we get that

Now let us consider the triangle OSA right angled at S. Here in triangle OSA, base is SA, altitude is OS and hypotenuse is OA.
Now let us consider the formula Pythagoras Theorem, sum of squares of two sides of a right-angled triangle is equal to square of hypotenuse.
So, using it we get,

Now substituting the value of SA from above, we get,
Question Image

Now, let us consider the triangle OPS right angled at S. Here in triangle OSP, base is SP, altitude is OS and hypotenuse is OP.
From the above figure we can see that the side SP is,
Question Image

Now let us consider the formula Pythagoras Theorem, sum of squares of two sides of a right-angled triangle is equal to square of hypotenuse.
So, using it we get,
Question Image

Now, from equations (2) and (3), we get,
Question Image

Now, let us substitute this value in equation (1). Then we get,
Question Image

So, the correct Ans is “Option 3”.
So, option 3 is correct.

Watch 3-min video & get full concept clarity

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th