Question

if PQ=QR=14cm then what is the length of the tangent RT?​

Answer 1

Answer:

use therom 6.7

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Step-by-step explanation:

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Answer 2

Given:

PQ=QR=14cm

To find:

The length of RT

Solution:

The required length of RT is 20 cm, approximately.

We can obtain the length by using the Pythagoras theorem.

We know that RT is tangent to the smaller circle and so, it is perpendicular to OT.

Since, PQ=14 cm and PO=OQ as O bisects PQ, the value of OQ=1/2 of PQ

OQ=PO=14/2=7cm

PQ is the smaller circle's diameter and OT is also the radius.

So, OQ=OT=7 cm

Now, in ΔOTR, angle T=90°.

Using the Pythagoras theorem,

$OT^{2} +RT^{2} =OR^{2}$

The length of OR=OQ+QR

=7+14=21 cm

On putting the values, we get

$7^{2} +RT^{2} =21^{2}$

49+$RT^{2}$=441

$RT^{2}$=441-49

$RT^{2}$=392

RT=19.79 cm

So, RT≈20 cm

Therefore, the required length of RT is 20 cm, approximately.