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In a ∆ABC, AD is the bisector of ∠A. (i) If AB = 6.4cm, AC = 8cm and BD = 5.6cm, find DC. (ii) If AB = 10cm, AC = 14cm and BC = 6cm, find BD and DC. (iii) If AB = 5.6cm, BD = 3.2cm and BC = 6cm, find AC. (iv) If AB = 5.6cm, AC = 4cm and DC = 3cm, find BC. |
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Answer» (i) It is give that AD bisects ∠A. Applying angle – bisector theorem in ∆ ABC, we get: BD/DC = AB/AC ⇒ 5.6/DC = 6.4/8 ⇒ DC = 8×5.6/6.4 = 7 cm (ii) It is given that AD bisects ∠A. Applying angle – bisector theorem in ∆ ABC, we get: BD/DC = AB/AC Let BD be x cm. Therefore, DC = (6- x) cm ⇒ x/ 6−x = 10/14 ⇒ 14x = 60-10x ⇒ 24x = 60 ⇒ x = 2.5 cm Thus, BD = 2.5 cm DC = 6-2.5 = 3.5 cm (iii) It is given that AD bisector ∠A. Applying angle – bisector theorem in ∆ ABC, we get: BD/DC = AB/AC BD = 3.2 cm, BC = 6 cm Therefore, DC = 6- 3.2 = 2.8 cm ⇒ 3.2/2.8 = 5.6/AC ⇒ AC = 5.6×2.8/3.2 = 4.9 cm (iv) It is given that AD bisects ∠A. Applying angle – bisector theorem in ∆ ABC, we get: BD/DC = AB/AC ⇒ BD/3 = 5.6/4 ⇒ BD = 5.6×3/4 ⇒ BD = 4.2 cm Hence, BC = 3+ 4.2 = 7.2 cm |
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