Question

If QT is 9 and TP is 8 Find the length of the following:

RP
RT
RS​

Answer 1

i. RP = 17

ii. RT = 15

iii. RS = 30

Explanation:

Given that; QT = 9 and TP = 8.

From the diagram, join R to P. Thus RP = QP (radius of the circle)

RP = QT + TP

= 9 + 8

RP = 17

Applying Pythagoras theorem to triangle TRP;

RT =
`\sqrt{(RP)^(2) - (TP)^(2) }`

=
`\sqrt{17^(2) - 8^(2) }`

=
`√(225)`

= 15

∴ RT = 15

But, RT = TS = 15.

So that;

RS = 15 + 15

= 30

RS = 30

Therefore; RP = 17, RT = 15 and RS = 30.