Wednesday, March 28, 2012

Puzzle 43 - Locus of midpoints

Two circles ${C_1},\,{C_2}$ with different radii are given in the plane touching each other externally at $T$. Consider points $A$ on ${C_1}$ and $B$ on ${C_2}$, such that $AB$ subtends right angle at $T$. Find the locus of midpoints of all such segments $AB$.

nasser ali said...

the commen tangent

Surya said...
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nagasrinivas m p said...

y-axis

Lohit KSG said...

it is the common tangent passing through the point T.

Vidyamanohar Sharma said...

If you a draw a circle with this mid point as center and its distance from origin as the radius, the common chord of this circle with the two given circles must be perpendicular. The locus comes out to be a circle

Vidyamanohar Sharma said...