Question

In the given figure if OP.OQ = OR.OS,then show that /_OPS =/_ORQ and /_OQR = OSP.

Answer 1

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Answer 2

CORRECT QUESTION

In the given figure if OP × OQ = OR × OS,then show that ∠OPS =∠ORQ and ∠OQR = ∠OSP.

ANSWER

∠OPS =∠ORQ

∠OPS =∠ORQ And,

∠OPS =∠ORQ And, ∠OQR = ∠OSP

GIVEN

OP × OQ = OR × OS

TO FIND

∠OPS =∠ORQ and ∠OQR = ∠OSP.

SOLUTION

We can simply solve the above problem as follows;

In ΔOPS and ΔQRO

OP × OQ = OR × OS (Given)

We can also write it as;

OP/OR = OS/OS.

Since, Ratio of corresponding sides of the triangles is same.

ΔOPS ~ ΔOQR

Therefore,

∠OPS =∠ORQ

∠OPS =∠ORQ And,

∠OPS =∠ORQ And, ∠OQR = ∠OSP

(Corresponding angles of similar triangles are equal to each other. )

Hence, Proved.

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