Question

Find ∠OQR ∠RST ∠TRQ
∠ROQ = 48

Answer 1

Given

• ∠ROQ = 48°

Find

• ∠OQR, ∠RST, ∠TRQ

Solution

We see that SR is a diameter, therefore Δ SRT is right triangle with ∠STR = 90°

∠ROQ, ∠RST and ∠TRQ all intercept the same arc RT

∠ROQ is twice the ∠RST and ∠TRQ as the central angle:

• ∠RST = ∠ROQ = 2*∠TRQ ⇒ ∠RST = ∠TRQ = 48°/ 2 = 24°

PQ is tangent to circle, therefore:

• PQ⊥SR ⇒ ∠OQR = 90°