Question

In the given circle chords BD and AC intersect at the centre P of the circle and making two pairs of vertically opposite angles .The measure of angle BPC is ------- degree. *​

Answer 1

Answer:

Answer

To prove ,PA×PB=PC×PD

Consider △PCA and PBD

∠PCA=∠PBD (Angle in the same segment)

∠APC=∠BPD (Vertically opposite angles)

△PCA∼△PBD (AA Similarity\right)

P lies outside the circle,

∠PCA+∠CAB=180

0

(Linear pair)

∠CAB+∠PDB=180

0

(Opposite angles of a cyclic)

∠PAC=∠PDB

In △PCA and △PBD

∠PAC=∠PDB (proved above)

∠APC=∠DPB (common)

∠PCA∼∠PBD (AA similarity)

Hence

PD

PA

=

PB

PC

PA×PB=PC×PD

Hence proved

Answer 2

Bro this is my 2 id of FF

1. 89800319
2. 1061304516