Question

PQ is a chord of Length 4.8 cm of a circle of radius 3 cm. t The tangent at P and Q intersect at point T as shown in the figure. Find the length of TP.

Answer 1

Answer:

Hence the length of TP is $TP = 4cm$.

Step-by-step explanation:

Our question is: PQ is a chord of Length 4.8 cm of a circle of radius 3 cm. t The tangent at P and Q intersect at point T as shown in the figure. Find the length of TP.

Let y be equal to TR and x be equal to TP.  

Thus, we can say that the line that is perpendicular to the line that connects the center to T is PR + RQ.

We know that PQ = 4.8 cm, then PR + RQ = 4.8  cm.

That is the same as saying that PR + PR = 4.8 cm.

From that we conclude that PR = 2.4 cm.

Therefore, in right triangle ΔPOR, using Pythagoras theorem, we have:

$PO^{2} = OR^{2} + PR^{2} \\ 3^{2} =OR^{2} +(2.4)^{2} \\ OR^{2} = 3.24\\ OR = 1.8 cm$

Now, in the right triangle ΔTPR:

$TP^{2} = TR^{2} + PR^{2} \\ x^{2} =y^{2}+(2.4)^{2}  \\ x^{2} =y^{2}+5.76$

Now in the right triangle ΔTPQ:

$TO^{2} =TP^{2} +PO^{2} \\ (y + 1.8)^{2}= x^{2}  + 3^{2} \\ y^{2} + 3.6y= x^{2} +5.76$

Thus, solving the last two equations, we get:

$x = 4cm\\ y = 3.2cm$

∴$TP = 4cm$

Hence the length of TP is $TP = 4cm$.

Answer 2

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