Question

In a circle AB, CD are two chords,meet at the point P. PA=16,PB=2,PD=6 find PC​

Answer 1

Answer:

(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

Step-by-step explanation:

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