Question

In the adjoining figure, the pair of tangents AP and AQ are O P 5 cm A Q drawn from an external point A to a circle with centre O are perpendicular to each other. If the length of tangent AP is 5 cm, then the radius of the circle is (1) 10 cm
(2) 7.5 cm
(3) 5 cm
(4) 2.5 cm

Answer 1

Join OP and then OA that bisect angle A then use tan45 is equal to P/B then u got OP =5 cm

Answer 2

Answer:

$\boxed{(3)\:5cm}$

Step-by-step explanation:

Since AP and AQ are tangents, two radii drawn from the center O, will meet the tangents at the point P and Q at right angles.

This implies the angle at the center is also 90°.

$\:<\:O + <\:A =180\degree$

$\Rightarrow \:<\:O =180\degree -90\degree$

$\Rightarrow \:<\:O =90\degree$

A line drawn from A to O bisects the angles at A and O.

This implies that, triangle APO and AQO are isosceles triangle.

Hence |OP|=|AP|=5cm

Therefore the radius is 5cm

See diagram