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In the figure, the circles with centers ...

In the figure, the circles with centers P and Q touch each other at R.A line passing through R meets the circles at A and B respectively.
Find `/_RQB` if `/_PAR=35^(@)`

Text Solution

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`/_PAR=35^(@)" " "……"(" Given ")`
`:.` From (i),(ii) and (iii),
`/_PRA=/_QRB=/_QBR=35^(@)" " "……(iv)`
In `triangle QRB`,
`/_QRB=/_QBR=/_RQB= 180^(@)" " "……."(" Sum of all angles of a triangle is " 180^(@) )`
`:.35^(@)+35^(@)+/_RQB=180^(@)" " "......."[" From (iv) "]`
`:. 70^(@)+/_RQB=180^(@)`
`:./_RQB=180^(@)-70^(@)`
`:./_RQB=110^(@)`
`/_RQB=110^(@)`.
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