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Mathematics

Chords AC and BD intersect each other at point P.

Chords AC and BD intersect each other at point P. Concise Mathematics Solutions ICSE Class 10.

Assertion (A) : PA x PC = PB x PD.

Reason (R) : Δ APD ∼ Δ BPC

Chords AC and BD intersect each other at point P. Concise Mathematics Solutions ICSE Class 10.

⇒PAPB=PDPC\Rightarrow \dfrac{PA}{PB} = \dfrac{PD}{PC}

  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 Δ APD and Δ BPC,

⇒ ∠APD = ∠BPC (Vertically opposite angles are equal)

⇒ ∠ADP = ∠BCP (Angles in same segment are equal)

∴ Δ APD ∼ Δ BPC (By A.A. similarity)

Corresponding sides of similar triangles are proportional.

⇒APPB=PDPC\Rightarrow \dfrac{AP}{PB} = \dfrac{PD}{PC} ……..(1)

So, reason (R) is true.

Solving (1),

⇒ AP x PC = PD x PB

So, assertion (A) is true and R is the correct reason for A.

Hence, option 3 is the correct option.

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