In ΔABC, we have ∠A = 60° and ∠B = 70°. Is the vertex C inside or outside the circle with diameter AB?

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Solution

Given: In ΔABC, ∠A = 60° and ∠B = 70°

Using angle sum property:

∠A + ∠B + ∠C = 180°

⇒ 60° + 70° + ∠C = 180°

⇒ 130° + ∠C = 180°

⇒ ∠C = 180° − 130°

= 50°

We know that angle in a semi circle is a right angle.

If AB is the diametre of the circle then ∠C should be equal to 90°.

However, here ∠C is less than 90°. Therefore, vertex C will lie outside the circle.

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Similar questions

In the quadrilateral ABCD, we have AB = 3 cm, BC = 4 cm, AC = 5 cm, ∠A = 120°, ∠C = 70°. If we draw the circle with AC as diameter, which of the four vertices of ABCD would be inside the circle? Which of them would be outside this circle? Is any vertex on the circle? What about the circle with BD as diameter.

In the figure , D is the centre of the circle and C is a point on the semi-circle with diameter DA. BC is a tangent through B.

If DB = 1 cm and AB = 3 cm, then $∠ C D B$ = _____

Q. Construct

∆

ABC, in which

∠

B =

70^{°}

∠

C =

60^{°}

, AB + BC + AC = 11.2 cm.

Q. Construct

∆

ABC such that

∠

B = 70

°

∠

C = 60

°

and AB + BC + CA = 10.5 cm.

Using ruler and compasses only:

i) Construct a $Δ$ ABC in which BC = 6cm, $∠$ ABC = 120 $^{\circ}$ and AB = 3.5 cm.

ii) In the above figure draw a circle with BC as diameter. Find a point P on the circumference of the circle that is equidistant from AB and BC. Measure the $∠$ BCP.

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