Question

If the angle between two tangents drawn from a point P to a circle of radius ‘a’ and centre ‘O’ is 90°, then OP = ______ 

Options

• `2asqrt2`

• `asqrt2`

• `a/sqrt2`

• `5asqrt2`

Answer 1

If the angle between two tangents drawn from a point P to a circle of radius ‘a’ and centre ‘O’ is 90°, then OP = `underline(asqrt2)`.

Explanation:

From point P, two tangents are drawn

OT = a (given)

Also, line OP bisects the RPT

Therefore,

 TPO = RPO = 45º

Also

OT is perpendicular to PT.

In the right triangle OTP

sin 45° = `"OT"/"OP"`

⇒ `1/sqrt2 = a/"OP"`

⇒ OP = `asqrt2`