Question

A point P is 13 cm from the centre of the circle. The length of the tangent drawn from P to the circle is 12cm. Find the radius of the circle.

• A. The angle subtended by AB at P and Q are either equal or supplementary.
• B. The sum of the angle subtended by AB at P and Q is always equal two right angle.
• C. The angle subtended at P and Q by AB are always equal.
• D. The sum of the angle subtended at P and Q is equal to four right angles

Answer 1

The correct option is A

The angle subtended by AB at P and Q are either equal or supplementary.

Since,
tangent to a circle is perpendicular to the radius through the point of contact
So, $\angle OTP={90}^0$
So, in triangle OTP
$(OP{)}^2=(OT{)}^2+(PT{)}^2$
${13}^2=(OT{)}^2+{12}^2$
$(OT{)}^2={13}^2-{12}^2$
$O{T}^2=25$
$OT=\sqrt{25}$
$OT=5$
So, radius of the circle is 5 cm