In the picture below, the radius of the circle is 15 cm. ∠QOR=120°. Select the statements that are true.
PQ = 15√3 cm
PR = 15√3 cm
Given, ∠QOR=120°
Therefore, ∠QPR=60° [∠QOR+∠QPR=180°]
∠QPO=30° [∠QPO=12∠QPR]
∠QOP=60° [∠QOP+∠QPO+∠OQP=180°]
In a right angled triangle where the angles are 30,60, 90, the sides are divided in the ratio 1:√3:2
Hence in △ POQ,
PO = 2 x OQ
= 2 x 15 = 30 cm
PQ2=302−152
PQ2=900−225
PQ2=675
PQ = PR = 15√3 cm [Tangents from the same point are equal in length]