Question

Chords AD and BC when produced meet at exterior point P.

Assertion (A): PD × AD = PC × BC

Reason (R): In triangles PAB and PCD,

∠PAB = ∠PCD ⇒ △PAB ∼ △PCD

⇒ `(PD)/(PB) = (PC)/(PA)`

पर्याय

• 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

A is false, R is true.

Explanation:

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.

⇒ `(PD)/(PB) = (PC)/(PA)`

∴ Reason (R) is true.

⇒ PD × PA = PC × PB

∴ Assertion (A) is false.

∴ A is false, R is true.