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In the given figure PA and PB are tangen...

In the given figure PA and PB are tangents to a circle with centre O. if `angleAPB= (2x +3)^@` and `angleAOB= (3x +7)^@`. then find the value of x.

Text Solution

Verified by Experts

As tangents from an external point are perpendicular to radius of the circle,
`:. /_OAP = /_OBP = 90^@`
Now, in quadrilateral `OAPB`,
`/_OAP+/_APB+/_OBP+/_BOA = 360^@`
`/_90^@+2x+3+90^@+3x+7 = 360^@`
`5x+10 = 180^@`
`x = 170/5`
`=>x = 34`
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