In the figure, the sides AB, BC and CA of a triangle ABC, touch a circle at P, Q and R respectively. IF PA = 4cm, BP = 3 cm and AC = 11 cm, then the length of BC (in cm) is ____
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In the figure, the sides AB...
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Asked on October 15, 2019 by
Nishchita Parmar
In the figure, the sides AB,BC and CA of a triangle ABC, touch a circle at P,Q and R respectively. If PA=4 cm, BP=3 cm and AC=11 cm, then the length of BC (in cm) is:
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As given
PA=4cm
BP=3cm
∴AB=4+3=7cm
AC=11cm
As PA and RA is two tangents from same external point A
∴RA=PA=4cm
⇒RC=AC−RA
⇒RC=11−4=7cm
As RC and QC is two tangents from same external point C
∴QC=RC=7cm
As BP and BQ is two tangents from same external point B
∴BP=BQ=3cm
Then BC=QC+BQ
⇒BC=7+3=10cm
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