Draw a circle with radius 2.5cm and draw a rhombus with one angle 50 degree, all four sides touching the circle.
Answers
We know that the central angle of the smaller arc between the two points on a circle and the angle between the tangents at these points are supplementary.
∠ ECF + ∠ EOF = 180°
⇒ ∠ EOF = 180° − 50° = 130°
We also know that any tangent to circle is perpendicular to the radius to the point of contact.
∴ ∠ OFC = ∠ OGB = ∠ OHD = ∠OEC = 90°
We will use these measurements to construct the required figure.
The steps of construction are as follows:
1) Draw a circle with centre O and radius, OF = 3 cm.
2) Draw ∠ OFX of measure 90° at point F by taking
OF as the base. Extend ray XF downwards.
3) Draw ∠ EOF of measure 140° at point O by taking
FO as the base.
4) Draw ∠ OEC of measure 90° at point E by taking
OE as the base. Extend CE downwards.
5) Extend the line segments EO and OF such that they intersect the circle at points G and H respectively.
6) Draw ∠ OGB of measure 90° at point G by taking OG as the base, where B is a point on line FX . Extend BG downwards.
7) Draw ∠ OHD of measure 90° at point H by taking
OH as the base, where D is a point on ray CE .
8) Extend line segment DH to intersect ray BG at point A.