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→Circles Tangents Problems
Draw the following sketch and do the calculations for the evaluation questions. The sketch shows the two main dimensions of a standard 400 metres running track.
Draw the following sketch and do the calculations for the evaluation questions. The sketch shows the two main dimensions of a standard 400 metres running track.
[[Image:KOER%20Circles_html_m210a6c46.png|650px|link=https://karnatakaeducation.org.in/KOER/en/index.php/File:KOER_Circles_html_m210a6c46.png]]
[[Image:KOER%20Circles_html_m210a6c46.png|650px|link=]]
====Evaluation====
====Evaluation====
#Calculate the inside perimeter of this shape.
#Calculate the inside perimeter of this shape.
=== [[Circles_Constructions]] ===
=== [[Circles_Constructions]] ===
== [[Circles Tangents Problems]] ==
=== Concept #7 Tangents ===
A line which touches a circle at exactly one point is called a tangent line and the point where it touches the circle is called the point of contact.
==== Properties of tangent ====
The tangent at any point of a circle is perpendicular to the radius through the point of contact. We can also conclude that at any point on a circle there can be one and only one tangent.
*Explain the theorem that if two segments from the same exterior point are tangent to a circle, then they are congruent.
*Solve for an unknown in a problem involving tangents.
*Apply properties of tangents to solve problems involving triangles circumscribed about a circle.
==== Tangents from a point outside the circle ====
The lengths of two tangents from an external point are equal.
The tangents drawn from an external point to a circle are equally inclined to the line joining the point to the centre of the circle.
==== Secant ====
A line which intersects the circle in two distinct points is called a secant line (usually referred to as a secant).
==== Touching circles ====
[[Image:KOER%20Circles_html_m5edc23ab.gif|link=https://karnatakaeducation.org.in/KOER/en/index.php/File:KOER_Circles_html_m5edc23ab.gif]]
[[Image:KOER%20Circles_html_m202ccc14.gif|link=https://karnatakaeducation.org.in/KOER/en/index.php/File:KOER_Circles_html_m202ccc14.gif]]
[[Image:KOER%20Circles_html_m5d49d71b.gif|link=https://karnatakaeducation.org.in/KOER/en/index.php/File:KOER_Circles_html_m5d49d71b.gif]]
==== Common tangents ====
Common tangents are lines or segments that are tangent to moret han one circle at the same time.
==== Direct common tangents ====
The centres of the circles lie on the same side of the common tangent.(dct)
[[Image:KOER%20Circles_html_m202ccc14.gif|link=https://karnatakaeducation.org.in/KOER/en/index.php/File:KOER_Circles_html_m202ccc14.gif]]
[[Image:KOER%20Circles_html_m244a7f98.png|link=https://karnatakaeducation.org.in/KOER/en/index.php/File:KOER_Circles_html_m244a7f98.png]]
==== Transverse common tangents ====
The centres of the circles lie on either side of the common tangent(tct)
[[Image:KOER%20Circles_html_m6e667170.png|link=https://karnatakaeducation.org.in/KOER/en/index.php/File:KOER_Circles_html_m6e667170.png]]
'''Evaluation'''
1.How many direct common tangents can be drawn to 2 intersecting circles and 2 separate circles?
2.Can you draw tct to 2 intersecting circles?
3. How many umber of tangents to a circle which are parallel to a secant ?
4. How many number of tangents that can be drawn through a point which is inside the circle ?
==== [[Circles Tangents Problems]] ====
To construct Transverse common tangents to two circles.
To construct Transverse common tangents to two circles.