2 circles Γ and Σ, with centers O and P, respectively, are such that P lies on Γ. Let A be a point on Σ, and let M be the midpoint of AP. Let B be another point on Σ, such that AB||OM. Then prove that the midpoint of AB lies on Γ.
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Ayushakj
26.02.2016 06:31
Let $AB$ intersect Γ at $C$ Join $PC$ In $\triangle APC$ $MS$ $\parallel AC$ Also $M$ is mid point.Hence $PS=SC$. In circle Γ.(bigger circle) $PS=SC$, Hence $OS \perp PC$ $MS$ $\parallel AC$ Hence $PC \perp AB$ SO $AC=BC$
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debasish123
06.10.2016 10:15
Oh you are right
Geoclid
20.11.2021 04:58
My step-by-step solution in great detail, very beginner-friendly. Enjoy!