Question

What is PN?

Answer 1

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