2015 · Q58
The point O is equidistant from die three sides of a triangle ABC. Consider the following statements:
- 1OAC+ OCB+ OBA=90^{}
- 2BOC=2 BAC
- 3The perpendiculars drawn from any point on OA to AB and AC are always equal
Which of the above statements are correct ?
Elementary MathematicsCircles
- A1 and 2 only
- B2 and 3 only
- C1 and 3 only
- D1, 2 and 3
Explanation
O is the incentre: angleOAC + angleOCB + angleOBA = (A + B + C)/2 = 90 (statement 1 true); but angleBOC = 90 + A/2, not 2A in general (statement 2 false); any point on the bisector OA is equidistant from AB and AC (statement 3 true). So 1 and 3 only, option (c). Note: one published key lists (d), but statement 2 holds only when A = 60 deg.