Question

If tangents QR, PR, PQ are drawn respectively at A, B, C to the circle circumscribin
and acute angled ΔABC, so as to form another ΔPQR, then the ∠RPQ is equal to
(a) ∠BAC
(b) 180° - ∠BAC
(c) (180° - ∠BAC)
(c) 1/2 (180 - ∠BAC)
(d) 180° -2 ∠BAC


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Answer 1

Answer:

180(0)−2∠BAC

When drawn lines from centre O to points B and C, ∠OBP and ∠OCP are 90(0)

Thus ∠BOC = 180(0)−∠RPQ and ∠BOC=2×∠BAC.

Thus solving we get ∠RPQ = 180(0)−2∠BAC.