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 find the length PX , AZ and QY.

Answer 1

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

$\Rightarrow$ c - a = -1 ......,(iv)

equation (iv) + equation (i) gives :

c - a + a + c = -1 + 7

$\Rightarrow$ 2c = 6

$\Rightarrow$ 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