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In figure, if PQR is the tangent to a ci...

In figure, if PQR is the tangent to a circle at Q whose centre is O, AB is a chord parallel to PR and `angleBQR=70^(@)` then `angleAQB` is equal to

A

`20^(@)`

B

`40^(@)`

C

`35^(@)`

D

`45^(@)`

Text Solution

Verified by Experts

The correct Answer is:
B
Given, AB||PR

`:.angleAQB =angleBQR=70^(@)` [alternate angles]
Also, QD is perpendicular to AB and QD bisects AB.
In `DeltaQDA and DeltaQDB`, `angleQDA=angleQDB` [each `90^(@)`]
AD=BD
QD=QD [common side]
`:.DeltaADQ=DeltaBDQ` [by SAS similarity criterion]
Then `angleQAD=angleQBD` [CPCT.....(i)]
Also `angleABQ=angleBQR` [altermat interior angle]
`:.angleABQ=70^(@)` `[:' angleBQR=70^(@)]`
Hence, `angleQAB=70^(@)` [from Eq. (i)]
Now, in `DeltaABQ`, `angleA+angleB+angleQ=180^(@)`
`rArrangleQ=180^(@)-(70^(@)+70^(@))=40^(@)`
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