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Triangles

In the given ...

Question

In the given figure, AD is the external bisector of $∠ E A C,$ intersects BC produced to D. If AB = 12 cm, AC = 8 cm and BC = 4 cm, find CD.

10 cm

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6 cm

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8 cm

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9 cm

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Solution

The correct option is C 8 cm
$\frac{A B}{B D} = \frac{A C}{C D} \frac{12}{B C + C D} = \frac{8}{C D} \frac{12}{4 + C D} = \frac{8}{C D} \Rightarrow C D = 8 c m$

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In the given figure, QR is parallel to AB and DR is parallel to QB. If PD = 4 cm and PA = 9 cm, then PQ = ____.

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