If OA and OB are the two radii and PA and PB are tangents. give a special name to the quadrilateral OBPA and justify your answer
Answers
Answer:
Formula used.
⇒ Perpendicular of tangent through point of contact pass through centre of circle
⇒ Sum of all angles of quadrilateral is 360°
⇒ Diagonals of square bisect each other at 90°
Solution.
Join AB and OT
In quadrilateral OATB
As OA and OB are perpendicular to each other
∠AOB = 90°
If tangents from point A and B are drawn
Then;
∠OAT = ∠OBT = 90°
Sum of all angles of quadrilateral is 360°
∠OAT + ∠OBT + ∠AOB + ∠ATB = 360°
90° + 90° + 90° + ∠ATB = 360°
∠ATB = 360° - 270°
= 90°
All angles of quadrilateral are 90°
Hence quadrilateral can be either square or rectangle
OA = OB ∵ (Both are radius of same circle)
If adjacent sides are equal
Then given quadrilateral is a square
In square diagonals are equal
Hence AB = OT
And diagonal bisect each other at 90°
Answer:
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