﻿ The locus of the middle points of the chords of the circle of radius r which subtend an angle π/4 at any point on the circumference of the circle is a concentric circle with radius equal to : Kaysons Education

# The Locus Of The Middle Points Of The Chords Of The Circle Of Radius r which Subtend An Angle π/4 At Any Point On The Circumference Of The Circle Is A Concentric Circle With Radius Equal To

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## Question

### Solution

Correct option is

Equation of the circle be x2 + y2 = r2. The chord which subtends an angle π/4 at the circumference will subtend a right angle at the centre. Chord joining (r, 0) and (0, r) subtends a right angle at the centre so (h,k) the mid-point of the chord is (r/2, r/2) and locus of (hk) is x2 + y2 =r2/2.

#### SIMILAR QUESTIONS

Q1

The locus of a point which moves such that the tangents from it to the two circles x+ y2 – 5x – 3 = 0 and 3x2 + 3y2 + 2x + 4y – 6 = 0 are equal is

Q2

If the two circles x2 + y2 + 2gx + 2fy = 0 and x2 + y2 + 2g1x + 2f1y = 0 touch each other, then

Q3

If two lines a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 cut the coordinates axes in concyclic points, then

Q4

The locus of the point which moves in a plane so that the sum of the squares of its distances from the lines ax + by + c = 0 and

bx – ay + d = 0 is r2, is a circle of radius.

Q5

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Q6

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Q7

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y = mx + c, then

Q8

The coordinates of two point P and Q are (2, 3) and (3, 2) respectively. Circles are described on OP and OQ as diameters; O being the origin, then length of the common chord is

Q9

The circle x2 + y2 – 6x – 4y + 9 = 0 bisects the circumference of the circle x2 + y2 – (λ + 4)x – (λ + 2)y + (5λ + 3) = 0 if λ is equal to

Q10

The lengths of the tangents from two points A and B to a circle are l and l’ respectively. If the points are conjugate with respect to the circle, then (AB)2 is equal to