Question

Chords AC and BD intersect each other at point P.

Assertion (A): PA × PC = PВ × PD

Reason (R): Δ APD ∼ Δ BPC

`(PA)/(PB) = (PD)/(PC)`

Options

• A is true, R is false.

• A is false, R is true.

• Both A and R are true and R is the correct reason for A.

• Both A and R are true and R is the incorrect reason for A .

Answer 1

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

Explanation:

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.

⇒ `(AP)/(PB) = (PD)/(PC)`        ....(1)

So, reason (R) is true.

Solving (1),

⇒ AP × PC = PD × PB

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