Question

In the given figure, PT is a tangent to the circle with centre O and radius r. If ∠POT = 45°, then the length of OP is:

Options

• `rsqrt2`

• `sqrt2r`

• 2r

• r²

Answer 1

`rsqrt2`

Explanation:

Given: OT = r

∠POT = 45°

Since PT is a tangent,

OT ⊥ PT

Use cosine in a right triangle OPT 

Cos 45° = `(OT)/(OP)`

`1/sqrt2 = r/(OP)`

OP = `rsqrt2`