| In the figure AABC is circumscribed touching the circle at P
Q and R. If AP = 4 cm, BP = 6 cm and AC = 12 cm, find the
length of BC
Answers
Answer:
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refer the reference diagram uploaded above for better understanding
Step-by-step explanation:
so here triangle abc circumscribed adjoining circle such that the circle touches the triangle abc at points p,q and r
so thus ab bc and ac are tangents to this circle
so here ap and ar are tangent segments drawn from external point A
pb and bq are tangent segments drawn from external point B
cr and cq are tangent segments drawn from external point C to adjoining circle
thus by tangent segment theorem
we get
ap=ar=4 cm
pb=bq=6 cm
cr=cq (1)
so here ac=12 cm
so thus ac=ar+cr (a-r-c)
thus cr=12-4
ie cr=8 cm
so thus cq=8 cm from (1)
so bc=bq+cq (b-q-c)
=6+8
=14cm
thus the length of bc is 14 cm