The sides
AB
,
BC
, and
AC
of a △ABC are tangent to a circle at points P, Q, and R respectively. Find AP, PB, BQ, QC, CR, and RA if AB = 10 cm, BC = 12 cm, and CA = 5 cm.
Answers
Given : AB , BC & AC Sides of a △ABC are tangent to a circle at points P, Q, and R respectively. AB = 10 cm, BC = 12 cm, and CA = 5 cm.
To find : AP, PB, BQ, QC, CR, and RA
Solution:
AP = AR ( Equal Tangents)
BP = BQ ( Equal Tangents)
CQ = CR ( Equal Tangents)
AB = AP + BP = 10
BC = BQ + CQ = 12
CA = CR + AR = 5
Adding all
AP + BP + BQ + CQ + CR + AR = 10 + 12 + 5
=> 2( AP + BP + CR) = 27
=> AP + BP + CR = 13.5
=> AP + BP = 10
=> CR = 3.5 & CQ = 3.5
AR = AC - CR = 5 - 3.5 = 1.5
=> AP = 1.5
BQ = BC - CQ = 12 - 3.5 = 8.5
BP = 8.5
AP = AR = 1.5 cm
BP = BQ = 8.5 cm
CQ = CR = 3.5 cm
Learn More:
ABC is right angled at A. The sides AB, BC and AC are the tangents to
https://brainly.in/question/12215786
A triangle has two sides along the coordinate axes and the third side ...
https://brainly.in/question/12360782