Q. 65.0( 1 Vote )

Find the locus of centres of circles which touch two intersecting lines.

Answer :


In Δ YXO and Δ ZXO,
∠ OYX = ∠ OZX (= 90°)
XO = XO (Common)
OY = OZ = radius
Δ YOX ≅ Δ ZOX (By SAS congruence)
∴ ∠ YXO = ∠ ZXO
∴ Locus of the centre is a straight line bisecting them between two intersecting lines.

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