1
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 :
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 :
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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
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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