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A circle with center O has a radius of 12 cm and a chord PQ of length 10 cm. If OS is perpendicular to PQ, what is the length of OS?

Mathematics

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  • Given: Circle with center O, OR = 12 cm, chord PQ = 10 cm, OS ⊥\perp PQ.
  • Find: Length of OS.

  1. Understand the properties of a chord perpendicular to the radius.

    A line segment drawn from the center of a circle perpendicular to a chord bisects the chord. Since OS ⊥\perp PQ, S is the midpoint of PQ.

    PS=SQ=PQ2=102=5 cmPS = SQ = \frac{PQ}{2} = \frac{10}{2} = 5 \text{ cm}

  2. Identify the right-angled triangle and

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