QP is a tangent to circle with centre O . If OQ= 4cm and angle OQP=30degree, then find the length of QP.
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Given, PQ is a chord of a circle with center O. Also, ∠QPT = 60°.
let x be the point on the tangent PT.
Now, ∠QPT + ∠QPX = 180° [Linear pair]
⇒ ∠QPX = 180° - ∠QPT = 180° - 60° = 120°
Again, ∠QPX = ∠PRQ [Alternate segment theorem]
⇒ ∠PRQ = 120
let x be the point on the tangent PT.
Now, ∠QPT + ∠QPX = 180° [Linear pair]
⇒ ∠QPX = 180° - ∠QPT = 180° - 60° = 120°
Again, ∠QPX = ∠PRQ [Alternate segment theorem]
⇒ ∠PRQ = 120
fiza57:
pq is atangent
find length of PQ
bt saif have done wrong he had assumed pq as chord
yes
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