Question

in fig if AB = 29cm, AD = 23cm, angle B = 90degree and DS = 5 cm then find the radius of the circle​

Answer 1

Answer:

Step-by-step explanation:

Given that DS = 5 cm;

Since DS and DR are tangents from the same external point to the circle, DS = DR = 5 cm

Since AD = 23 cm, AR = AD - DR = 23 - 5 = 18 cm.

Similarly, AR and AQ are the tangents from the same external point to the circle and hence AR = AQ = 18 cm.

Since AB = 29 cm, BQ = AB - AQ = 29 - 18 = 11 cm.

Since CB and AB are the tangents to the circle, angle OPB and angle OQB is equal to 90 degrees.

Given that angle B is 90 degrees and hence angle POQ is also equal to 90 degrees and hence OQBP is a square.

Since BQ is 11 cm, the side of the square OQBP is 11 cm

the side of the square is the radius of the circle and hence radius of the circle is 11 cm.

Answer 2

Answer:

The value of the radius of the circle is 11cm.

Step-by-step explanation:

Given AB=29cm, AD = 23cm

       and ∠B = 90°, DS = 5cm

Since BQ and BQ are tangents from B on the circle and ∠B = 90° then

∠P = 90°, ∠Q = 90°  ( Since tangents from point B on P and Q).

PBQO is a square with ∠B = 90°.

So, PB = BQ = QO = OP = r(radius of circle)

Also, DS and DR are tangents from D on the circle at the points S and R.

     So, DS= DR = 5cm

            AR = AD- DR = 23- 5 = 18cm

Since AR and AQ are the tangents from A on the points R and Q on the circle then

          AR = AQ = 18cm

Since AB= 29cm and AQ = 18cm

then Radius BQ = AB - AQ = 29-18 = 11cm

Know more about Parts of Proof of Geometry:

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