In the figure a circule with center o is inscribed in rhadulateral ABCD such that ,it touches the side to be BC,AB,AD,CD at point P,Q,R and S respectively. If AB=29 cm,AD=23cm,DS=5cm and angle B =90cm find the radius of the circle
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given ds = 5 cm;
as....ds and dr are tangents from the same external point to the circle ds = dr = 5 cm
as..ad= 23 cm ar = ad - dr = 23 - 5 = 18 cm.
again..
.ar and aq are the tangents from the same external point to the circle and hence ar = aq = 18 cm.
as... ab = 29 cm...bq = ab - aq = 29 - 18 = 11 cm.
as.... cb and ab are the tangents to the circle, angle opb and angle oqb is equal to 90 degrees
ginen that angle b is 90 degrees and hence angle poq is also equal to 90 degrees and hence oqbp is a square.
as... bq is 11 cm, the side of the square oqbp is 11 cm
∴11 cm is the answer
as....ds and dr are tangents from the same external point to the circle ds = dr = 5 cm
as..ad= 23 cm ar = ad - dr = 23 - 5 = 18 cm.
again..
.ar and aq are the tangents from the same external point to the circle and hence ar = aq = 18 cm.
as... ab = 29 cm...bq = ab - aq = 29 - 18 = 11 cm.
as.... cb and ab are the tangents to the circle, angle opb and angle oqb is equal to 90 degrees
ginen that angle b is 90 degrees and hence angle poq is also equal to 90 degrees and hence oqbp is a square.
as... bq is 11 cm, the side of the square oqbp is 11 cm
∴11 cm is the answer
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