Question

In the figure <A = 34 °, <C = 54° a) <D =? b) <B =? And. C) Prove that Triangle PAC and Triangle PDB are similar. d) If PA = 8 cm, PD = 6cm and PC = 4 cm, see AB.




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Answer 1

PROPERTY :

Angles subtended by a chord/arc on same side of a circle at circumference are same.

now

arc BC subtends angles CAB and CDB at circumference on same side.

so

< CDB = < CAB

< D = 34°

similarly arc AD subtends angles B and C at circumference

so

B = C = 54°

remaining angle

APC = DPB

so ∆ APC ~ ∆ DPB

thus

PA/PD = PC/PB

PB = PC x PD/PA

= 4 x 6/8

= 3

AB = PA + PB

= 8 + 3

= 11