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Valentin [98]
1 year ago
14

circle o is inscribed in triangle rst such that it is tangent at points m,n, and p. if rp is 7, rt is 17 and sm is 5, then what

is the length of side st?
Mathematics
1 answer:
zloy xaker [14]1 year ago
7 0

Answer:

The length of side st is 15.

Step-by-step explanation:

A tangent is a straigth line that touches a circle externally at a point on the circumference. Considering one of its properties that tangents from the same point to a fixed point outside a circle are equal.

Then,

     /rn/ = /rp/

    /tm/ = /tn/

   /sm/ = /sp/

But, /rp/ = 7, /rt/ = 17 and /sm/ = 5.

Then,

 /rt/ = /rn/ + /tn/

17 = 7 + /tn/ (∵ /rp/ = /rn/ = 7)

⇒ /tn/ = 10

Since /nt/ = 10, then /tm/ = 10 (/tm/ = /nt/)

So that,

 /st/ = /sm/ + /tm/

     = 5 +10

 /st/ = 15

The length of side st is 15.

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