Advertisements
Advertisements
Question
In the given figure, ΔABC is an equilateral triangle. Find m∠BEC.
Advertisements
Solution
It is given that, Δ ABC is an equilateral triangle
We have to find `m angle BEC`
Since Δ ABC is an equilateral triangle.
So `angle A + angle B + angle C = 180°`
And
`angle A = angleB = angleC` = 60° …… (1)
Since, quadrilateral BACE is a cyclic qualdrilateral
So , `angle A + angleE = 180°` (Sum of opposite angles of cyclic quadrilateral is 180° .)
`60° + angle E = 180°`
`angle E = 120°`
Hence
`m angle BEC = 120°`
APPEARS IN
RELATED QUESTIONS
In two concentric circles, prove that all chords of the outer circle which touch the inner circle are of equal length.
Fill in the blanks:
Segment of a circle is the region between an arc and __________ of the circle.
In the given figure, AB is a chord of length 16 cm of a circle of radius 10 cm. The tangents at A and B intersect at a point P. Find the length of PA.
In the given figure, a circle inscribed in a triangle ABC, touches the sides AB, BC and AC at points D, E and F Respectively. If AB= 12cm, BC=8cm and AC = 10cm, find the length of AD, BE and CF.
ABC is a right triangle in which ∠B = 90°. If AB = 8 cm and BC = 6 cm, find the diameter of the circle inscribed in the triangle.
In the given figure, the area enclosed between the two concentric circles is 770 cm2. If the radius of the outer circle is 21 cm, calculate the radius of the inner circle.
Draw a circle of radius of 4.2 cm. Mark its center as O. Takes a point A on the circumference of the circle. Join AO and extend it till it meets point B on the circumference of the circle,
(i) Measure the length of AB.
(ii) Assign a special name to AB.
In the figure, O is the centre of the circle, and ∠AOB = 90°, ∠ABC = 30°. Then find ∠CAB.
In the following figure, O is the centre of the circle. Name all chords of the circle.
In the given figure, O is the centre of the circle. If ∠AOB = 145°, then find the value of x.
