Question

ABCD is a quadrilateral such that angle D=90. A circle C(0,r) touches the side AB, BC,CD and DA at P,Q,R and S respectively. If BC=38 cm, CD=25cm and BP =27 cm. Find r.

Answer 1

Step-by-step explanation:

    Given ABCD is a quadrilateral such that angle D=90. A circle C(0,r) touches the side AB, BC,CD and DA at P,Q,R and S respectively. If BC=38 cm, CD=25 cm and BP =27 cm. Find  

• ABCD is a quadrilateral where in   angle D = 90 degree.  
• We have BC = 38 cm,  
• CD = 25 cm and  
• BP = 27 cm
• From the above question we have,
• Since the tangents from an external point are equal,
• BQ = BP = 27 cm
• So BC = 38 cm
• Or QC + BQ = 38
• Or QC + 27 = 38
• QC = 38 – 27
• QC = 11 cm
• Since the tangents from an external point are equal
• Therefore QC = CR = 11 cm
• CD = 25 cm
• RD + CR = 25
• RD + 11 = 25
• Or RD = 25 – 11
• Or RD = 14 cm
• OS and OR are radii of the circle.
• Since tangents from an external point are equal,  
• DS = RD = 14 cm

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Answer 2

Answer:

14

Step-by-step explanation:

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