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melamori03 [73]
2 years ago
13

In adjoining figure a circle is inscribed in the quadrilateral ABCD given that BC is equal to 38 cm cube is equal to 27 cm and B

C equal to 25 cm and that ad is perpendicular to DC find the radius of the circle.​

Mathematics
2 answers:
vodka [1.7K]2 years ago
8 0

Answer:

14 cm

Step-by-step explanation:

<u>Given</u>

  • BQ = BR, AQ = AP, CR = CS, DP = DS = OP = OS
  • BQ = 27 cm
  • BC = 38 cm
  • DC = 25 cm

<u>Solving</u>

  • BQ = BR (given)
  • ⇒ BR = 27 cm
  • BC = BR + CR
  • 38 = 27 + CR
  • CR = 11 cm
  • ⇒ CS = 11cm
  • DC = DS + CS
  • 25 = 11 + DS
  • ⇒ DS = 14 cm
  • But, DS = OS and OP (radii)
  • ⇒ Radius = 14 cm

lukranit [14]2 years ago
5 0

<h3>Radius = 14cm</h3>

Step-by-step explanation:

Let O be the centre of the circle. Since P and S are the points of contact of tangents AD and DC respectively, OP ⊥ AD and OS ⊥ DC

Also, AD ⊥ DC (given), therefore, OPDS is a square.

BR = BQ = 27cm...(tangents from an external point to a circle are equal in length)

therefore, CR = CB - BR = (38 - 27)cm = 11cm

SC = CR = 11 cm...(tangents from an external point) therefore, DS = DC - SC = (25 - 11) cm = 14 cm.

therefore,

Radius of a circle = OP = DS = 14 cm...(therefore, OPDS is a square).

<h3>Hope it helps you!! </h3>
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