In the diagram of circle o, what is the measure of ∠abc?

Asked by wiki @ 09/11/2020 in Mathematics viewed by 332 People

27°
54°
108°
120°

Answered by wiki @ 09/11/2020

Given:

Given that a circle O with two tangents BA and BC.

The major arc AC is 234°

The minor arc AC is 126°

We need to determine the measure of ∠ABC

Measure of ∠ABC:

We know the property that, "if a tangent and a secant, two tangents or two secants intersect in the interior of the circle, then the measure of angle formed is one half the difference of the measures of the intercepted arcs."

Hence, applying the above property, we have;

$\angle ABC=\frac{1}{2}( major \widehat{AC} - minor \widehat{AC})$

Substituting the values, we get;

$\angle ABC=\frac{1}{2}( 234^{\circ} -126^{\circ})$

$\angle ABC=\frac{1}{2}( 108^{\circ})$

$\angle ABC=54^{\circ}$

Thus, the measure of ∠ABC is 54°

Hence, Option b is the correct answer.

What is the measure of angle cab in circle o

Asked by maham237 @ 20/05/2021 in Mathematics viewed by 365 persons

24 48 72 96

What is the measure of angle cab in circle o?

Asked by maham237 @ 22/12/2020 in Mathematics viewed by 408 persons

What is the measure of angle CAB in circle O? 24 48 72 96

In the diagram of circle a, what is the measure of ∠xyz?

Asked by wiki @ 14/11/2020 in Mathematics viewed by 400 persons

35° 70° 75° 140°

In the diagram, is a diameter of circle o. if the slope of is , what is the slope of ?

Asked by maham237 @ 25/12/2020 in Mathematics viewed by 429 persons

In the diagram, AC is a diameter of circle O. If the slope of BC is -1/2 , what is the slope of AB? See attachment.

Find the measures of the indicated angles in circle o

Asked by maham237 @ 19/05/2021 in Mathematics viewed by 368 persons

Which statement is NOT true? (The figure is not drawn to scale.) b = 106 d = 37 a = 53 c = 73

In circle o, ae and fc are diameters. arc ed measures 17°. what is the measure of ?

Asked by maham237 @ 22/12/2020 in Mathematics viewed by 340 persons

In circle O, AE and FC are diameters. Arc ED measures 17°. What is the measure of ? °

A circle is inscribed in a triangle abc

Asked by admin @ 24/08/2021 in Math viewed by 309 persons

A circle is inscribed in a triangle ABC, having sides 8 cm , 10 cm and 12 cm. Find AD , BE and CF ( these 3 are altitudes of …

O is the centre of circle of radius 5cm

Asked by admin @ 20/08/2021 in Math viewed by 288 persons

In figure O is the centre of a circle of radius 5 cm.T is a point such that OT=13CM and OT intersects the circle at E.if AB is the tangent …

Abc is an isosceles triangle inscribed in a circle

Asked by admin @ 17/08/2021 in Math viewed by 353 persons

ABC Is an isosceles triangle inscribed in a circle. If AB=AC=25 cm and BC=14 cm. Find the radius of the circle.

Ab is a chord of circle with centre o

Asked by admin @ 17/08/2021 in Math viewed by 295 persons

AB is a chord of a circle with centre O. At B, a tangent PB is drawn such that its length is 24cm. The distance of P from centre is …

An equilateral triangle abc is inscribed in a circle

Asked by admin @ 13/08/2021 in Math viewed by 284 persons

An equilateral triangle ABC is inscribed in a circle with centre o find measure of angle boc

A triangle abc is drawn to circumscribe a circle

Asked by admin @ 10/08/2021 in Math viewed by 271 persons

a triangle ABC is drawn to circumscribe a circle of radius 4cm such that the segments BD and DC which BC is divided by the point of contact the are …

O is the centre of the circle of radius 5cm

Asked by admin @ 03/08/2021 in Math viewed by 282 persons

In figure O is the centre of a circle of radius 5 cm.T is a point such that OT=13CM and OT intersects the circle at E.if AB is the tangent …

Diagram of a circle

Asked by maham237 @ 11/02/2021 in Mathematics viewed by 284 persons

here is a diagram of a straightedge and compass construction. c is the center of one circle,and b is the center of the other. explain why length of segment BD …