Using ruler and a compass only construct a semi-circle with diameter BC = 7cm. Locate a point A on the circumference of the semicircle such that A is equidistant from B and C. Complete the cyclic quadrilateral ABCD, such that D is equidistant from AB and BC. Measure ∠ADC and write it down.
Prove that the circle drawn on any one of the equal sides of an isosceles triangle as diameter bisects the base.
Calculate the area of the shaded region, if the diameter of the semicircle is equal to 14 cm. Take `pi = 22/7`
In the following figure, AB is the diameter of a circle with centre O.
If chord AC = chord AD, Prove that:
(i) arc BC = arc DB
(ii) AB is bisector of ∠CAD.
Further, if the length of arc AC is twice the length of arc BC, find : (a) ∠BAC (b) ∠ABC
In the figure, given alongside, AB ∥ CD and O is the centre of the circle. If ∠ADC = 25°; find
the angle AEB give reasons in support of your answer.
In the given figure, AB is a diameter of the circle. Chord ED is parallel to AB and ∠EAB = 63°. Calculate
(i) ∠EBA (ii) ∠BCD
Prove that the perimeter of a right triangle is equal to the sum of the diameter of its incircle and twice the diameter of its circumcircle.
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