Question

69. The length of the two tangents of a
circle from a point is 30 cm each. If the
tangents form an angle of 60° with
each other, the distance between the
point and the centre of the circle is
meble
[A] 60 cm
[B] 35 cm
[C] 2013 cm
[D] 302 cm​

Answer 1

luv uh meri jaan ;p ♥️_♥️ umaaah

Answer 2

The distance between the point and center of the circle is 35 cm.

• Given,

        lengths of the tangents = 30 cm

            PQ = PR = 30 cm

• Angle between tangents = 60°

               ∠QPR = 60°

• Let O be the center of the circle.
• OP bisects ∠QPR.

                  ∠OPR = ∠OPQ = 30°

• Also PQ⊥OQ ⇒ ∠OQP = 90°

• In ΔOPQ,

                  $cos30=\frac{PQ}{OP}$

                  $\frac{\sqrt{3} }{2}=\frac{30}{OP}$

                  $OP\sqrt{3}=60$

                  $OP=\frac{60}{\sqrt{3} }$

                  OP = 34.64

                  OP≅35 cm