In an isosceles triangle ABC, with AB = AC, the bisectors of ∠ B and ∠ C intersect each other at O. Join A to O. Show that :
(i) OB = OC
(ii) AO bisects ∠ A
(i) It is given that in triangle ABC, AB = AC
∴ ∠ACB = ∠ABC (Angles opposite to equal sides of a triangle are equal)
∴\(\frac{1}{2}\) ∠ACB= \(\frac{1}{2}\) ∠ABC
∴ ∠OCB =∠OBC
∴ OB = OC (Sides opposite to equal angles of a triangle are also equal)
(ii) In ∆OAB and ∆OAC,
AO =AO (Common)
AB = AC (Given)
OB = OC (Proved above)
Therefore, ∆OAB ∆OAC (By SSS congruence rule)
∠BAO = ∠CAO (CPCT)
∴ AO bisects A.
A driver of a car travelling at \(52\) \(km \;h^{–1}\) applies the brakes Shade the area on the graph that represents the distance travelled by the car during the period.
Which part of the graph represents uniform motion of the car?