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13 Dec 2018, 02:35
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
54% (02:18) correct
46%
(02:23)
wrong
based on 174
sessions
History
Date
Time
Result
Not Attempted Yet
In the figure above, segments AD and AC divide ∠EAB into three nonoverlapping angles that are equal in measure. Axe AE and AB equal in length?
(1) AD = AC
(2) AC = CB
Attachment:
2018-12-13_1331.png [ 11.19 KiB | Viewed 5368 times ]
13 Dec 2018, 05:28
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Solution
Given:
- • ∠EAD = ∠DAC = ∠CAB = \(x^o\)
To find:
- • Whether AE = AB or not
Analysing Statement 1
“AD = AC”
- • So, In triangle ADC, ∠ADC = ∠ACD = \(
- (180 – x)/2
o Implies, ∠ADE = ∠ACB = \(180 – (90 – \frac{x}{2}) = 90 + \frac{x}{2}\)
• Thus,
- o In triangle AED, ∠AED = \(180 – x – (90 + \frac{x}{2}) = 90 – \frac{3x}{2}\)
o Similarly, in triangle ACB, ∠ABC = \(180 – x – (90 + \frac{x}{2}) = 90 – \frac{3x}{2}\)
• In triangle AEB, ∠AEB = ∠ABE = \(90 – 90 – \frac{3x}{2}\)
• Therefore, AB = AE
Hence, statement 1 is sufficient
Analysing Statement 2
“AC = CB”
- • So, In triangle ABC, ∠ABC = ∠CAB = x
- o Implies, ∠ACB = 180 – x - x = 180 – 2x
In triangle ACD, ∠ADC = 180 – x – 2x = 180 – 3x
- • Implies, ∠ADE = 180 - ∠ADC = 3x
In triangle ADE, ∠AED = 180 – x – 3x = 180 – 4x
In triangle AEB, ∠AEB =180 - 4x and ∠ABC = x
- • These angles may or may not be equal
• Therefore, we cannot say whether AB = AE or not
Statement 2 is not sufficient
Hence, the correct answer is Option A.
Answer: A
21 Sep 2023, 19:28
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