In the given figure, PA and PB are tangents to a circle from an external point P such that PA=4 cm and `angleBAC=135^(@).` Find the length of dhord AB.

In the given figure, PA and PB are tangents to a circle from an extern

1.	In the given figure, PA and PB are tangents to a circle from an external point P such that PA=4 cm and `angleBAC=135^(@).` Find the length of dhord AB.
Answer» We have, `angleBAC=135^(@)` `:." "anglePAB=180^(@)-135^(@)=45^(@)" "`(L.P.A)...(1) But since `PA=PB=4`(length of tangents from an external point are equal) …(2) `implies" "anglePBA=anglePAB" "`(angles opposite to equal sides are equal) `implies" "anglePBA=45^(@)" "`[from (1)] Now, in `trianglePAB,` `angleAPB=180^(@)-(45^(@)+45^(@))" "`(angle sum property) `=90^(@)` In right `trianglePAB,` by Pythagoras theorem, `AB^(2)=PA^(2)+PB^(2)=(4)^(2)+(4)^(2)=32` `:." "AB=sqrt(32)cm=4sqrt(2)cm` Hence, the length of chord AB is `4sqrt(2)cm.`

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In the given figure, PA and PB are tangents to a circle from an external point P such that PA=4 cm and `angleBAC=135^(@).` Find the length of dhord AB.

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