The points represented by the complex numbers a, b, c lie on a circle with center O and radius r. The tangent at c cuts the chord joining the points a, b at z. Show that z = 
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
|a| = |b| = |c| = r
z, a, b are collinear
⇒ z( 
– 
) – 
(a – b) + 
= 0
⇒ z 
( a 
= r 2 )
⇒ 
(b – a)r 2 – 
(a – b) + 
= 0
⇒ z + 
– (a + b) = 0...(1)
Sum of complex slope = 0
Also 
+ 
= 0
⇒ 
z – |c| 2 + c 
– |c| 2 = 0
⇒ c 
= 2|c| 2 – 
z
⇒ c 
= 2r 2 – 
|c| = r
or 
= 
...(2)
so by (1)
z + ab 
– (a + b) = 0
z = 
= 
H.P.
──────────────────────────────────────────────────────────────────────────────────────────
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems