The chord of a circle is √3. Times its radius. The angle subtended by this chord at minor arc is k times the angle subtended at major arc. What is the value of K
Answers
The value of K is 2.
Step-by-step explanation:
Radius OA = r, chord AB = √3 r
<ACB = 'a' deg , < ADB = ka deg
& < AOB = 2<ACB = 2a deg
Perpendicular OM from the centre O to the chord AB bisects the chord
AM = √3 r /2 & <AOM = a deg
In triangle AMO
Sin a = AM/AO = √3r/2 / r = √3/2
=> a = 60 deg …………………. (1)
Since, a + ka = 180 deg ( opposite angles of a cyclic quadrilateral)
=> 60 + 60 k = 180 ( by 1)
=> 60 k = 120
=> k = 2
Thus the value of K is 2.
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Answer:
The value of K is 2.
Step-by-step explanation:
Radius OA = r, chord AB = √3 r
<ACB = 'a' deg , < ADB = ka deg
& < AOB = 2<ACB = 2a deg
Perpendicular OM from the centre O to the chord AB bisects the chord
AM = √3 r /2 & <AOM = a deg
In triangle AMO
Sin a = AM/AO = √3r/2 / r = √3/2
=> a = 60 deg …………………. (1)
Since, a + ka = 180 deg ( opposite angles of a cyclic quadrilateral)
=> 60 + 60 k = 180 ( by 1)
=> 60 k = 120
=> k = 2
Thus the value of K is 2.
Step-by-step explanation:
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