Given, equation of circle is x2+y2=25..(i) ∴ Equation of tangent to the given circle at R(3,4) is given by 3x+4y=25...(ii) (by the rule, xx1+yy1=25⇒3x+4y=25 ) For OP, we must put y=0 and for OQ, put x=0 in Eq. (ii).
∴OP=
25
3
and OQ=
25
4
∴PQ=
125
12
∵OP+PQ+QO=25 ∴ In centre of
∆OPQ=(
OP×0+PQ×0+OQ×
25
3
OP×
25
4
+PQ×0+QO×0
) =(
25
4
×
25
3
25
,
25
3
×
25
4
25
)=(
25
12
,
25
12
)
According to the question, incentre of △OPQ= centre of the required circle r= radius of the required circle which is passing through origin. =√(
