Question

If PQR is a tangent to a circle at Q whose centre is O, AB is a chord parallel to PR and ZBQR = 60°, then ZAQB is equal to o 60 P R [1 mark] O 60° O 90° O 30° 0 45°​

Answer 1

Answer:

if PQR is the tangent to a circle at Q whose centre is O, AB is a chord parallel to PR and ∠BQR = 70°, then ∠AQB is equal to 40°. ⇒ ∠AQB = 180° – 140° = 40°.

Step-by-step explanation:

As OQ⊥ PR

(radius ⊥ tangent) & AB∣∣PR

⇒AB⊥OL

and perpendicular from centre to chord bisects the chord.

⇒AL=BL,

∠QLB=∠QLA

& LQ=LQ\Rightarro$$ By SAS

congruency, ΔQLA≅ΔQLB

⇒∠AQL=∠BQL=20o (90o−70o)

⇒∠AQB=40o.

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