Question

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

Answer 1

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 2

Answer:

Hi I hope all are fine in this pandemic .... and pray for all those are suffering from corona+ praying for your mom dad that they stay well