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

3 cm, 4 cm, 5 cm

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4 cm, 5 cm, 3 cm

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3 cm, 5 cm, 4 cm

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4 cm, 3 cm, 5 cm

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Solution

The correct option is A
3 cm, 4 cm, 5 cm

Let, AX = AZ = a , QZ = QY = b , PX = PY = c

We know PA = a + c = 7 cm ..........(i) PQ = b + c = 8 cm .......(ii) QA = a + b = 9 cm .........(iii)

(ii) - (iii) $\to$ (c + b) - (a + b) = 8 - 9 $\to$ c - a = -1 ........(iv)

(iv) + (i) $\to$ (c - a) + (a + c) = -1 + 7 $\to$ 2 c = 6 ; c = 3 cm

subtituting c in (i) $\to$ a + 3 = 7 ; a = 4 cm

subtituting c in (ii) $\to$ 3 + b = 8 ; b = 5 cm.

so, PX = c = 3 cm ; AZ = a = 4 cm ; QY = b = 5 cm.

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