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# From a point P, 2 tangents PA & PB are drawn to a circle with centre O.If OP=diameter of the circle show that triangle APB is equilateral.

Asked by Annie(ST. MARY'S CONVENT SCHOOL) , on 23/2/11

Hi Rida!

The given information can be represented using a figure as

â‡’ âˆ OPA = 30Â°
Similarly, it can be proved that âˆ OPB = 30Â°.
Now, âˆ APB = âˆ OPA + âˆ OPB = 30Â° + 30Â° = 60Â°
In âˆ†PAB,
PA = PB  [lengths of tangents drawn from an external point to a circle are equal]
â‡’âˆ PAB = âˆ PBA     ...(1)   [Equal sides have equal angles opposite to them]
âˆ PAB + âˆ PBA + âˆ APB = 180Â°    [Angle sum property]
â‡’âˆ PAB + âˆ PAB = 180Â° â€“ 60Â° = 120Â°  [Using (1)]
â‡’2âˆ PAB = 120Â°
â‡’âˆ PAB = 60Â°      ...(2)
From (1) and (2)
âˆ PAB = âˆ PBA = âˆ APB = 60Â°
âˆ´ âˆ†PAB is an equilateral triangle.

Cheers!

Posted by gopal.mohanty...on 24/2/11

This conversation is already closed by Expert

sir is it necessary to use trigo in this??? i mean the tangents ARE ALWAYS inclined wid each othe at 60degreees rite? so can 't v write dis simply???????

Posted by Divya Kaur(GURU HARKRISHAN PUBLIC SCHOOL) on 10/3/11

u too r ryt !!

Posted by Afzal Husain(D A V Public school) on 10/3/11

no ...............m sorry ....................itz not always at 60 degrees ! it can vary  !!

Posted by Afzal Husain(D A V Public school) on 10/3/11