We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.

Point P splits a diameter of a circle into segments of lengths 2 and 6. What is the shortest distance from the center of this circle to a chord through P that makes a 30-degree angle with the diameter?

 Apr 30, 2019

See the following, SydSu.....



A perpendicular bisector drawn to the chord from the center of the circle will be the shortest distance from the center to the chord.....


Let the equation of the circle be x^2 + y^2  = 16


The equation of the line containing the chord  is  y  = (1/sqrt(3)) ( x + 2)


Call the point of intersection of the bisector and the chord, M


Then....AMP  will form a right triangle.....with angle AMP  = 90°   and AP the hypotenuse  = 2


Then...AM  will be the distance we are looking for.....and since this side of the right triangle is opposite the 30°  it will be (1/2) of AP  =  1



cool cool cool

 May 1, 2019

22 Online Users