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Mathematics

In the given figure, PQ is parallel to TR, then by using condition of similarity:

  1. PQRT=OPOT=OQOR\dfrac{PQ}{RT} = \dfrac{OP}{OT} = \dfrac{OQ}{OR}

  2. PQRT=OPOR=OQOT\dfrac{PQ}{RT} = \dfrac{OP}{OR} = \dfrac{OQ}{OT}

  3. PQRT=OROP=OQOT\dfrac{PQ}{RT} = \dfrac{OR}{OP} = \dfrac{OQ}{OT}

  4. PQRT=OPOR=OTOQ\dfrac{PQ}{RT} = \dfrac{OP}{OR} = \dfrac{OT}{OQ}

In the given figure, PQ is parallel to TR, then by using condition of similarity: Similarity of Triangles, RSA Mathematics Solutions ICSE Class 10.

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Answer

Given,

ΔPOQ and ΔROT

∠POQ = ∠TOR [vertically opposite angles are equal]

∠OPQ = ∠ORT [Alternate interior angles are equal]

∴ ΔPOQ ∼ ΔROT (By A.A. axiom)

We know that,

The ratio of corresponding sides in similar triangles are proportional.

PQRT=OPOR=OQOT\dfrac{PQ}{RT} = \dfrac{OP}{OR} = \dfrac{OQ}{OT}

Hence, option 2 is the correct option.

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