Check sibling questions

In the given figure, ∠ACB = ∠CDA, AC = 8cm, AD = 3cm, then BD is

(a) 22/3 cm   (b) 26/3 cm   (c) 55/3 cm   (d) 64/3 cm

This question is inspired from Question 17 - Sample Paper for 2020 Boards - Class 10 Sample Paper

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Question 30 In the given figure, ∠ACB = ∠CDA, AC = 8cm, AD = 3cm, then BD is (a) 22/3 cm (b) 26/3 cm (c) 55/3 cm (d) 64/3 cm Given ∠ACB = ∠CDA In Δ ACB and Δ ADC ∠ACB = ∠ADC ∠CAB = ∠DAC ∴ Δ ACB ∼ Δ ADC We know that Sides of similar triangle are in same proportion ∴ 𝐴𝐶/𝐴𝐷 = 𝐴𝐵/𝐴𝐶 Putting values 8/3 = 𝐴𝐵/8 8/3 = 𝐴𝐵/8 8/3 × 8 = AB 64/3 = AB AB = 𝟔𝟒/𝟑 Now, BD = AB − AD = 64/3 − 3 = (64 − 9)/3 = 𝟓𝟓/𝟑 cm So, the correct answer is (c)

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