- #1

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## Homework Statement

there is a circle with radius 9cm centred at o

segment oa is 15cm

ab, ca and pq are tangents to circle at points b,c and r respectively

find perimeter of triangle apq

## Homework Equations

## The Attempt at a Solution

i have solved the problem and got the right answer with two methods but i feel none of the methods is proper per say

method 1:

since the question is not imposing any restriction on the location of point r i assumed the perimeter is invariant with respect to r and hence let the segment pq fall on segment ca essentially the perimeter of two triangles is now just the two times the length of ac

ac is 12 cm by pythagoras hence the perimeter of triangle is 24 cm

a really crude method really dont think it is correct

method 2:

once with the assumption that the perimeter is invariant with respect to r

i shifted r right up to the point where da intersects the circle

then the triangle rpa is similar to triangle boa then rp is 9/2 and pa is 7.5 cm

then perimeter is once again 15 + 9 = 24 cm

however i feel my assumption is wrong and the question can be solved without the assumption so someone please help? thanks