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In triangle PQR, the bisector of angle QPR meets side QR at point S. If PQ = 10 cm and PR = 14 cm, what is the ratio PS : QR? (Note: find BD : DC or the ratio as given in options.)

1. 10 : 7
2. 5 : 7
3. 7 : 5
4. 7 : 10

Correct answer: 5 : 7

Solution

By the Angle Bisector Theorem, the bisector of angle A in triangle ABC divides BC such that BD/DC = AB/AC = 10/14 = 5/7. Therefore BD : DC = 5 : 7. The question's intended ratio is BD : DC (the two segments), which equals 5 : 7.

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