Question

In the given figure, PR, RT and PT are tangents to the circle at Q,
S and U respectively. If PR = (RT + 3) cm, PR = (PT + 1) cm and
perimeter of A PRT is 26 cm, then QR + RT equals to:
(A) 9 cm
(B) 7 cm
(C) 13 cm
(D) 11 cm​

Answer 1

Answer:

So as per understanding the question , We get to know the correct option for this question is option (D)

Step-by-step explanation:

The detailed solution of this question is as below [ Attached image ]

Hope it clears your doubt.

Thank You.

Answer 2

The value of RT+QR=11 cm

Step-by-step explanation:

$PR=RT+3$

$PR=PT+1$

$RT=PR-3$

$PT=PR-1$

Perimeter of triangle PRT=26 cm

Perimeter of triangle=PR+RT+PT

$PR+PR-3+PR-1=26$

$3PR-4=26$

$3PR=26+4=30$

$PR=\frac{30}{3}=10$

PR=10 cm

$RT=10-3=7cm$

$PT=10-1=9 cm$

Let PQ=x

QR=y and ST=z

PQ=PU=x

QR=RS=y

ST=TU=z

Reason: Two tangents are drawn from any external point on the circle are equal in length.

$x+y=10$..(1)

$y+z=7$...(2)

$x+z=9$...(3)

Adding equation (1) and equation(3)

$2x+y+z=19$

From equation (2)

$2x+7=19$

$2x=19-7=12$

$x=\frac{12}{2}=6$

Substitute the value of x in equation(1)

$6+y=10$

$y=10-6=4$

RT+QR=7+4=11 cm

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https://brainly.in/question/7752562:Answered by vedulkrishanchaitan