Question

two tangents PM and pn are draw to a circle with center o from an external point p. if <mpn =110°,then <omn​

Answer 1

Answer:

65°

Step-by-step explanation:

Given

PM and PN are tangents from point P

∠MPN = 110°

To Find

∠OMN

Solution

Since PM and ON are tangents then

PM┴OM & PN┴ON (since tangents are ┴ radius)

also PM = PN (tangents drawn from a point a equal in length)

Now in quadrilateral MONP

applying angle sum property we get

∠MON + ∠ONP + ∠MPN + ∠OMP = 360°

=> ∠MON + 90° + 110° + 90° = 360°

=> ∠MON = 70°

Now in ∆MNO

Since OM = ON (Radius of common circle)

Therefore ∠OMN = ∠ONM (angles opposite to equal sides are equal)

Now by applying angle Sum property in ∆MNO

we get ∠OMN + ∠MNO + ∠NOM = 180°

=> 2∠OMN = 180° - 70°

=> ∠OMN = 65°

Hope I made it clear

Happy Learning!