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Chapter 9: Q16. (page 337)

SR炉 is tangent to 鈯�P and 鈯�Q.

QT=6,TR=8,PR=30.

PQ=?,PS=?,ST=?

Short Answer

Expert verified

The required values are,

PQ=20,PS=18andST=16

Step by step solution

01

Step 1. Given information.

鈯�PAny SR炉 is tangent to 鈯�P and 鈯�Q. Also QT=6,TR=8andPR=30.

02

Step 2. Concept used.

Applying Pythagoras in triangle 螖RTQ to find the value of PQ.

Here, 螖RTQis right angle triangle,

QR2=62+82QR2=36+64QR鈥夆赌夆赌夆赌�=10

As value of ,

PQ=30鈭�10PQ=20

03

Step 3. Let ST be x and SP be y.

Here, TQ炉||SP炉

Then,

810=x20x鈥夆赌夆赌夆赌�=8鈰�鈥�2010x鈥夆赌夆赌夆赌�=16

Same way,

86=24yy鈥夆赌夆赌夆赌�=24鈰�鈥�68y鈥夆赌夆赌夆赌�=18

Therefore, the values are, PQ=20,PS=18andST=16.

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