Question

in any triangle ABC, if the angle bisector of angle A and perpendicular bisector of BC intersect, prove that they intercept on the circumcircle of the triangle ABC​

Answer 1

Step-by-step explanation:

In triangle ROQ,

OR-OQ as these are the radii of the circle.

So, we know that in an isosceles triangle, equal sides have equal opposite angles.

Therefore, ZORQ = 20°

Similarly, ZORP = 30°

ZPRQ = ZORQ+ZORP

Now,

=20+30=50⁰

We know that angle subtended by an arc of a circle at the centre is double the angle subtended by an arc at any point on the circumference, thus

ZPOQ = 2/PRQ ZPOQ = 2 x 50 = 100°