If in a triangle PQR, sin P, sin Q, sin R are in AP, then

Question

If in a triangle PQR, sin P, sin Q, sin R are in AP, then (A) the altitudes are in AP (B) the altitudes are in HP (C) the medians are in GP (D) the medians are in AP

Tardigrade Admin · Accepted Answer

By the law of sine rule, (a/ sin P ) = (b/ sin Q) = ( c/ sin R ) = k [ say] Also, (1/2), ap1 = triangle ⇒ ( 2 triangle /α) = p1 ⇒ p1 = (2 triangle / k sin P ) Similarly, p2 = ( 2 triangle / k sin Q ) and p3 = (2 triangle / k sin R ) Since, sin P, sin Q and sin R are in AP, hence p1, p2, p3 are in HP.

Q. If in a △ PQR, sin P, sin Q, sin R are in AP, then

the altitudes are in AP

the altitudes are in HP

the medians are in GP

the medians are in AP

By the law of sine rule, sin Pa​=sin Qb​=sin Rc​=k [ say] Also, 21​,ap1​=△⇒α2triangle​=p1​ ⇒p1​=k sin P2△​ Similarly, p2​=k sin Q2△​ and p3​=k sin R2△​ Since, sin P, sin Q and sin R are in AP, hence p1​,p2​,p3​ are in HP.

Q. If in a $△$ PQR, sin P, sin Q, sin R are in AP, then