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

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

4cm

5cm

6cm

answer is C.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

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