Two statements are missing reasons. What reasons can be used to justify both statements 2 and 3 ?

Question

asked Jun 14, 2020 121k views

2 Answers

Anothershrubery · Answer 1 · 2020-06-19T07:18:06+0000

Answer:

See explanation

Explanation:

The given circle has center O.

A, B,C, and D are points on the circumference of the circle.

We want to prove that:
$\angle A\cong \angle D$

We need to join to B and C as shown in the attachment.

Recall that angle subtended by arc BC at the center is twice the angle subtended at the circumference by the same arc.

This implies that:

$\angle O=2\angle A...(1)$

$\angle O=2\angle D...(2)$

The LHS of equation (1) and (2) are equal. Therefore the RHS are also equal.

This implies that:

$2\angle A=2\angle D$

$\therefore \angle A\cong \angle D$