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in given figure, figure two circle with centre A and B touch each other externally at C the length of PQ is ()​

In Given Figure Figure Two Circle With Centre A And B Touch Each Other Externally At C The Length Of PQ Is class=

Sagot :

Akifjwraaidn

SOLUTION :

The tangent at any point of Circle is perpendicular to the radius.

  • [tex]\; \angle ASP = \angle BTQ=90°[/tex]

In triangle ∆ ASP Apply Pythagoras theorem.

  • [tex]AS=AP²-PS²[/tex]

  • [tex]\implies AS= \sqrt{AP²-PS²} [/tex]

  • [tex]\implies AS= \sqrt{13 {}^{2} + 12 {}^{2} } [/tex]

  • [tex]\implies AS= \sqrt{25} cm[/tex]

  • [tex]\implies AS=5cm[/tex]

  • [tex]\implies{\boxed{{{AS=AC=5cm}}}}[/tex]

In triangle ∆ BTQ Apply Pythagoras theorem.

  • [tex]BT²=BQ²-TQ²[/tex]

  • [tex]\implies BT= \sqrt{BQ²-TQ²} [/tex]

  • [tex]\implies BT= \sqrt{5 {}^{2} - 3 {}^{2} } [/tex]

  • [tex]\implies BT= \sqrt{16} cm[/tex]

  • [tex]\implies BT=4cm[/tex]

  • [tex]\implies{\boxed{{{BT=BC=4cm}}}}[/tex]

ANSWER :

Therefore length of PQ is

  • [tex]PQ=PA+AC+BC+BQ [/tex]

  • [tex]\implies PQ = 13 + 5 + 4 + 5[/tex]

  • [tex]\implies PQ={\boxed{{{27cm}}}}\:(Answer)[/tex]

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