Question

3) In triangle ABC ∠B = 40◦
, ∠C = 50◦
. A circle is drawn on BC as the diametre.Where is A based
on this circle?
(a) In the circle (b) Outside the circle (c) Inside the circle (d) Cannot be determined

Answer 1

Answer:

c ) Inside the circle

Step-by-step explanation:

Angel b and angle c intersected inside the circle

means at point A so , answer is option 'c'

Answer 2

Given :    In triangle ABC ∠B = 40◦ , ∠C = 50◦

A circle is drawn on BC as the diameter

To Find : Where is A based on this circle?

(a)on the circle (b) Outside the circle (c) Inside the circle (d) Cannot be determined

Solution:

Inscribed Right Angle in a Circle Theorem

If an inscribed angle in a circle intercepts its diameter, so that the circle is divided into semicircles, the inscribed angle is a right angle.

If an inscribed angle in a circle is a right angle, that angle intercepts the diameter of the circle.

∠B = 40◦ , ∠C = 50◦

Sum of angles of a triangle = 180°

=> ∠A = 180° - 40° - 50°

=> ∠A  = 90°

BC is the side opposite and Diameter

so point A will lie on the circle using Inscribed Right Angle in a Circle Theorem

Hence point A lie on the circle

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