Question

prove that the line joining the midpoint of a chord to the center of a circle passes through th mid point of the corresponding minor arc

Answer 1

Answer:

Let the centre be O, chord be AB, the point of intersection P, and its production to the arc be Q.

As AP=AQ, OP is _|_ to AB.

So, QAP and QBP are right ∆s.

In these ∆s,

AP=BP(Given)

PQ=PQ(Common)

APQ=BPQ(Postulate 4)

So, the ∆s are congruent by SAS.

Thus, AQ=BQ(CPCT)

Therefore, the arcs are equal.

Answer 2

Answer:

Let the centre be O, chord be AB, the point of intersection P, and its production to the arc be Q.

As AP=AQ, OP is _|_ to AB.

So, QAP and QBP are right ∆s.

In these ∆s,

AP=BP(Given)

PQ=PQ(Common)

APQ=BPQ(Postulate 4)

So, the ∆s are congruent by SAS.

Thus, AQ=BQ(CPCT)

Therefore, the arcs are equal.

Step-by-step explanation: