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27 May 2020, 04:26
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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:
35%
(medium)
Question Stats:
65% (01:18) correct
35%
(01:19)
wrong
based on 122
sessions
History
Date
Time
Result
Not Attempted Yet
In triangle ABC, is AC^2 = AB^2 + BC^2 ?
(1) ∠BAC + ∠ACB = ∠ABC
(2) AB = BC
(1) ∠BAC + ∠ACB = ∠ABC
(2) AB = BC
Updated on: 28 May 2020, 06:37
Originally posted by rishab0507 on 27 May 2020, 05:41.
Last edited by rishab0507 on 28 May 2020, 06:37, edited 1 time in total.
Last edited by rishab0507 on 28 May 2020, 06:37, edited 1 time in total.
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In triangle ABC, is AC^2 = AB^2 + BC^2 ?
(1) ∠BAC + ∠ACB = ∠ABC
(2) AB = BC
Question stem is asking us whether ABC is right angled triangle or isocles right ∠ed triangle.
Statement 1 :
∠BAC and ∠ ACB can be a 30-60 and ∠ ABC 90, forming 30-60-90 triangle, which will fulfill pythgores theorem,
or can be 45-45-90 triangle which can fulfill pythagores theorem. So we get 2 answers,yes
Sufficient
Statement 2 :
As we are looking for 3-4-5 or 6-8-10 etc type triangles, if AB= BC, then we can't fulfill pythagores theo. It can be 45-45-90 or 30-30- 120 triangles : So answer will be no and yes
In Sufficient
IMO A
(1) ∠BAC + ∠ACB = ∠ABC
(2) AB = BC
Question stem is asking us whether ABC is right angled triangle or isocles right ∠ed triangle.
Statement 1 :
∠BAC and ∠ ACB can be a 30-60 and ∠ ABC 90, forming 30-60-90 triangle, which will fulfill pythgores theorem,
or can be 45-45-90 triangle which can fulfill pythagores theorem. So we get 2 answers,yes
Sufficient
Statement 2 :
As we are looking for 3-4-5 or 6-8-10 etc type triangles, if AB= BC, then we can't fulfill pythagores theo. It can be 45-45-90 or 30-30- 120 triangles : So answer will be no and yes
In Sufficient
IMO A
27 May 2020, 06:41
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Bunuel
Solution
Step 1: Analyse Question Stem
- • ABC is a triangle. (Shown below)
• We need to find if \(AC^2 = AB^2+ BC^2\)
- o The above equation represents the Pythagoras theorem for right angle.
- So basically, we need to find out whether triangle ABC is right angle or not.
Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE
Statement 1: ∠BAC + ∠ACB = ∠ABC
- • ∠BAC + ∠ACB + ∠ABC = 180° [sum of interior angles of a triangle = 180°]
- ⟹ 2∠ABC = 180°
⟹ ∠ABC = 90°
Statement 2: AB = BC
- • This statement only tell us that triangle ABC is isosceles, or ∠BAC = ∠ACB
- o However, we cannot conclude that the third angle is 90 degrees or ABC is a right angled triangle.
- o If ∠BAC = ∠ACB =35 degrees ⟹ ∠ABC = 180 – 70 = 110 degrees
- Then ABC is not right angled triangle.
- Then ABC is a right angled triangle.
Thus, the correct answer is Option A.
