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In the adjoining figure, O is the centre...

In the adjoining figure, O is the centre of a circle. If AB and AC are chords of the circle such that AB `=`AC ,`OP _|_ AB` and `OQ _|_ AC`, prove that `PB = QC`.

Text Solution

Verified by Experts

`AB=ACimplies(1)/(2)AB= (1)/(2) AC implies MB = NC`.
Also, `/_PMB = /_ QNC = 90^(@)`
Equal chords are equidistant from the centre `implies OM = ON`.
Also, `OP = OQ =` radius `implies OP -OM = OQ-ON implies PM =QN`
`:. Delta MPB ~= Delta DQCimplies PB=QC`
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