Question

Draw a circle of radius 4 cm. Construct a pair of tangents to it, the angle between which is ${60}^0$. Also justify the construction. Measure the distance between the centre of the circle and the point of intersection of tangents.

• A. 4 cm
• B. 6 cm
• C. 8 cm
• D. 10 cm

Answer 1

The correct option is C 8 cm

Join O and P.
Now, in triangles OPQ and OPR,
OP = OP (Common)
OQ = OR (radius of circle)
PQ = PR (tangents from single point)
Hence OPQ and OPR are congruent triangles.
$\angle OPQ=\angle OPR={30}^{\circ }$

Thus in triangle OPQ, $\frac{OQ}{OP}=Sin30$

OP = $\frac{4}{Sin30}$

OP = 8 cm