Question

Two tangents are drawn onto a circle with centre O and radius r, from an external point P. These tangents touch the circle at points A and B respectively. The triangle ABP is definitely a ______________ .

• A. Scalene triangle
• B. Isosceles triangle
• C. Equilateral triangle
• D. Right angled triangle

Answer 1

The correct option is B

Isosceles triangle

Refer to the following figure:

Consider $△AOPand△BOP$

$AO=BO$ [radius of the circle]

$\angle OAP=\angle OBP$ [right angle]

$OP=OP$ [common side]

Therefore the triangles are congruent. So, $AP=PB$. Hence in $△ABP,AP=PB$. So it is definitely an isosceles triangle.