Question

Write True or False:

If a chord AB subtends an angle of ${60}^0$ at the centre of a circle, the angle between the tangents at A and B is also ${60}^0$.

• A. True
• B. False
• C. Data Inadequate
• D. Ambiguous

Answer 1

The correct option is B False

Given-

PA & PB are tangents to the circle with centre O at A & B, respectively.

The chord AB subtends an angle ${60}^o$ at O.

To find out-

The assertion, $\angle APB={60}^o$ is true or false.

Justification-

PA & PB are tangents to the circle at A & B respectively.

$\therefore \angle PAO=\angle PBO={90}^o.$

Now, in the quadrilateral APBO,

$\angle PAO+\angle PBO+\angle AOB+\angle APB={360}^o$ ...(angle sum property of quadrilaterals)

$⟹{90}^o+{90}^o+{60}^o+\angle APB={360}^o$

$⟹\angle APB={120}^o$

$\therefore$ The assertion, $\angle APB={60}^o$, is false