Question

in a cirlcle AB,CD are two chords meeting at the same the point P,PA=16,PB=7,PD=4 THEN FINDS PC​

Answer 1

Step-by-step explanation:

Solution

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(i) In △PAC and △PDB,

∠BAC=180

∘

−∠PAC (linear pairs)

∠PDB=∠CDB=180

∘

−∠BAC

=180

∘

−(180

∘

−∠PAC)=∠PAC)

∠PAC=∠PDB ... (1)

∠APC=∠BPD [Common] ... (2)

We know that in a cyclic quadrilateral, the exterior angle is equal to the interior opposite angle.

Therefore, for cyclic quadrilateral ABCD.

consider ABCD ΔPAC and ΔPBD.

∠PCA=∠PBD .... (3)

∴ By AAA-criterion of similarity,

△PAC∼△DPB

(ii) △PAC∼△DPB

So, the corresponding sides of the similar triangles are proportional

PD

PA

=

PB

PC

⇒PA.PB=PC.PD