Question

In the given figure, the sides of the quadrilateral PQRS touches the circle at A,B,C and D. If RC = 4 cm, RQ = 7 cm and PD = 5cm. Find the length of PQ:
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Answer 1

$\large\underline{\sf{Solution-}}$

Given that,

• The sides of the quadrilateral PQRS touches the circle at A,B,C and D.

• RC = 4 cm, RQ = 7 cm and PD = 5cm.

We know, Length of tangents drawn from external point are equal.

Now, R is external point and RC and RB are tangents drawn from this external point.

$\rm\implies \:RC=RB$

$\rm\implies \:\boxed{ \rm{ \:RC=RB = 4 \: cm \: }}$

Now, It is given that RQ = 7 cm

So, $\rm \: RB + BQ = 7$

$\rm \: 4 + BQ = 7$

$\rm\implies \:\boxed{ \rm{ \:BQ \: = \: 3 \: cm \: }}$

Now, Q is external point and QA and QB are tangents drawn from this external point.

$\rm\implies \:\boxed{ \rm{ \:QA = QB = 3 \: cm \: }}$

Now, RP is external point and PA and PD are tangents drawn from this external point.

$\rm\implies \:\boxed{ \rm{ \:PA = PD = 5 \: cm \: }}$

Now, Consider

$\red{\rm \: PQ}$

$\rm \: = \: PA+AQ$

$\rm \: = \: 5 + 3$

$\rm \: = \: 8 \: cm$

Hence,

$\rm\implies \:\boxed{ \rm{ \:PQ \: = \: 8 \: cm \: }}$

Answer 2

Answer:

The length of PQ is 8 cm.

Step-by-step explanation:

Quadrilateral:

A quadrilateral is a four-sided polygon with four edges and four corners that is used in geometry. The Latin words quadri, a variation of four, and latus, meaning "side," are the source of the name.

Theorem: Two tangents traced from an outside point to a circle have identical lengths.

Given that RC = 4 cm, RQ = 7 cm, and PD = 5 cm

From the point P two tangents are drawn those are PD and PA.

The length PD and PA are the same according to the theorem.

Therefore PA = PD = 5 cm.

From the point R two tangents are drawn those are RB and RC.

The length RB and RC are the same according to the theorem.

Therefore RB = RC = 4 cm.

Again RQ = RB + BQ

7 = 4 + BQ

BQ = 3 cm.

From the point Q two tangents are drawn those are QA and AB.

The length QA and QB are the same according to the theorem.

Therefore QA = QB = 3 cm.

The length of PQ is PA + AQ = 5 + 3 cm = 8 cm.

To learn more about property of tangent click on the below link:

https://brainly.in/question/38972369

https://brainly.in/question/53884261

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