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Question

# In the given figure, the circles touch the lines at X , Y , Z , B , C and D. If PQ = 8cm , QA = 9cm and PA = 7cm, then the length PX , AZ and QY respectively are :

A

4 cm ; 3 cm ; 5 cm

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B

3 cm ; 5 cm ; 4 cm

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C

4 cm ; 5 cm ; 3 cm

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D

3 cm ; 4 cm ; 5 cm

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Solution

## The correct option is D 3 cm ; 4 cm ; 5 cm AX = AZ = a QZ = QD = b PX = PY = c ...........(Tangents in alternate segments are equal) We know, a + c = 7 ...........(i) c + b = 8 ...........(ii) a + b = 9 ...........(iii) equation (ii) - equation (iii) gives: c + b - a - b= 8 - 9 ⇒ c - a = -1 ......,(iv) equation (iv) + equation (i) gives : c - a + a + c = -1 + 7 ⇒ 2c = 6 ⇒ c = 3 cm ........... (v) Substituting (v) in (i) we get : a + 3 = 7 a = 4 cm Substituting (v) in (ii) we get : 3 + b = 8 b = 5 cm Hence, PX = c = 3 cm AZ = a = 4 cm QY = b = 5 cm

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