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Chords AD and BC one produce meet at exterior point P.

Chords AD and BC one produce meet at exterior point P. Concise Mathematics Solutions ICSE Class 10.

Assertion(A): PD x AD = PC x BC.

Reason(R): In triangles PAB and PCD.

∠PAB = ∠PCD ⇒ ΔPAB ∼ ΔPCD

⇒PDPB=PCPA\Rightarrow \dfrac{PD}{PB} = \dfrac{PC}{PA}

  1. A is true, R is false.

  2. A is false, R is true.

  3. Both A and R are true and R is correct reason for A.

  4. Both A and R are true and R is incorrect reason for A.

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Answer

In ΔPAB and ΔPCD,

⇒ ∠PBA = ∠PDC (Exterior angles of a cyclic quadrilateral is always equal to interior opposite angle)

⇒ ∠PAB = ∠PCD ((Exterior angles of a cyclic quadrilateral is always equal to interior opposite angle))

ΔPAB ~ ΔPCD (By A.A. axiom of similarity)

We know that,

Corresponding sides of similar triangles are proportional.

⇒PDPB=PCPA\Rightarrow \dfrac{PD}{PB} = \dfrac{PC}{PA}

∴ Reason (R) is true.

⇒ PD x PA = PC x PB

∴ Assertion (A) is false.

∴ A is false, R is true.

Hence, option 2 is the correct option.

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