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In the same circle, chord AB determines a 115° arc and chord AC determines a 43° arc. Find m∠BAC.

User Jay Zelos
by
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1 Answer

3 votes

Answer:

36° or 101°

Explanation:

Consider the figures given in the attachment.

Point C can be between A and B as shown in the left image of the attachment or outside AB chord as shown in the right image.

In both figures, ∠AOB = 115° and ∠AOC = 43°.

Both the triangles are isoceles triangle as OC and OA side is equal in ΔAOC and OA and OB is equal in ΔAOB.

In ΔAOC,

∠A + ∠O + ∠C = 180°

∠A = ∠C

∴ 2 ∠A =180-43=137°

∴∠A = 68.5

In ΔAOB,

∠A + ∠B + ∠O = 180°

∠A = ∠B

∴2 ∠A = 180-115=65°

∴∠A = 32.5°

For figure on the left side,

∠BAC = ∠OAC - ∠OAB = 68.5 - 32.5 =36°

For figure on right side,

∠BAC = ∠OAC + ∠OAB = 68.5 + 32.5 =101°

In the same circle, chord AB determines a 115° arc and chord AC determines a 43° arc-example-1
User Alexrussell
by
7.0k points
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