What is PN?

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Answer 1 · 2018-03-30T03:33:00

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Given that straight lines AS and AP intersect a circle of center M at #K&S and N&P# respectively.

Here #AN=7cm,AK=5cm and SK=17cm#

We are to find out the length of #PN#

Construction

#S,N and P,K# are joined,

Now #DeltaNSA and Delta KPA# are similar

since #angle KAP= angleNAS# are common.

#angle ASN = angle APK# are angles on same arc #NK# of the circle of center M

So relating the ratio of corresponding sides of similar triangles we can write

#(AP)/(AS)=(AK)/(AN)#

#=>(PN+AN)/(AK+SK)=(AK)/(AN)#

#=>(PN+7)/(5+17)=5/7#

#=>PN=5/7xx22-7~~8.71# cm