Question

Write true or false and give reasons for your answers.

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

• A. True
• B. False

Answer 1

The correct option is B False

Let us consider a circle with center $O$ and $AB$ be a chord.

So, $\angle AOB={60}^o$ [ Given ]

$AP$ and $BP$ are two intersecting tangents at point $P$ at point $A$ and $B$.

Tangents drawn at a point on a circle is perpendicular to the radius through the point of contact.

$\therefore$ $OA\perp AP$ and $OB\perp BP$

$\Rightarrow$ $\angle OAP=\angle OBP={90}^o$

In quadrilateral $AOBP,$

$\Rightarrow$ $\angle OAP+\angle OBP+\angle APB+\angle AOB={360}^o$

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

$\Rightarrow$ ${240}^o+\angle APB={360}^o$

$\Rightarrow$ $\angle APB={120}^o$

$\therefore$ The given statement is $False.$