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25 Apr 2019, 03:15
Kudos
Bookmarks
B
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:
48% (02:51) correct
52%
(02:38)
wrong
based on 42
sessions
History
Date
Time
Result
Not Attempted Yet
Quadrilateral ABCD is inscribed in a circle with angle BAC = 70°, angle ADB = 40°, AD = 4, and BC = 6. What is AC?
(A) \(3 + \sqrt{5}\)
(B) 6
(C) \(\frac{9\sqrt{2}}{2}\)
(D) \(8 - \sqrt{2}\)
(E) 7
(A) \(3 + \sqrt{5}\)
(B) 6
(C) \(\frac{9\sqrt{2}}{2}\)
(D) \(8 - \sqrt{2}\)
(E) 7
25 Apr 2019, 18:34
Kudos
Bookmarks
IMO B
if we draw the quadrilateral ,
amd calculate the angles ( especially using the property that angles in se segment by any chord are equal )
we can see that the triangle ABC will become an isoselece triangle with angles 70,70,40
so this way we can say that BC = AC = 6
award kudos if helpful
Posted from my mobile device
if we draw the quadrilateral ,
amd calculate the angles ( especially using the property that angles in se segment by any chord are equal )
we can see that the triangle ABC will become an isoselece triangle with angles 70,70,40
so this way we can say that BC = AC = 6
award kudos if helpful
Posted from my mobile device
10 Feb 2020, 00:43
Kudos
Bookmarks
Bunuel
Solution:
This question is based on the following property. Once, we understand what property to use. This question is not that difficult to solve.
- • Inscribed angles subtended by the same arc of a circle are equal.
Keeping this property in mind. Let's solve this question.
- • \(∠BAC = ∠BDC = 70\) [angle subtended by same arc BC]
• \(∠ACB=∠ADB= 40\) [angle subtended by same arc AB]
- In triangle ABC,
• \(∠ABC + ∠ACB+∠BAC = 180\)
• \(∠ABC= 180 – 70 – 40\)
• \(∠ABC = 70\)
• \(∠ABC = ∠BAC = 70\)
- • AC = BC
• BC = 6
- o AC = 6
