{"id":4949,"date":"2021-12-01T14:45:04","date_gmt":"2021-12-01T14:45:04","guid":{"rendered":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/?page_id=4949"},"modified":"2022-01-03T08:17:50","modified_gmt":"2022-01-03T08:17:50","slug":"concurrent-lines-point-of-concurrency-examples","status":"publish","type":"page","link":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/concurrent-lines-point-of-concurrency-examples\/","title":{"rendered":"Concurrent Lines – Point of concurrency – Examples"},"content":{"rendered":"

[et_pb_section fb_built=”1″ admin_label=”Section” module_class=”mainsec” _builder_version=”4.10.4″ _module_preset=”default” background_color=”#e0f2fd” z_index=”1″ custom_padding=”5px||5px||true|false” locked=”off” collapsed=”off” global_colors_info=”{}”][et_pb_row column_structure=”3_5,2_5″ custom_padding_last_edited=”on|phone” _builder_version=”4.10.8″ _module_preset=”default” background_color=”#FFFFFF” width=”100%” max_width=”1310px” custom_padding=”|51px|40px|51px|false|true” custom_padding_tablet=”” custom_padding_phone=”|40px|30px|40px|false|true” border_radii=”on|10px|10px|10px|10px” global_colors_info=”{}”][et_pb_column type=”3_5″ admin_label=”Column L” _builder_version=”4.9.10″ _module_preset=”default” global_colors_info=”{}”][et_pb_text admin_label=”Acute Angles
\n” _builder_version=”4.13.1″ _module_preset=”default” header_font=”|700|||||||” header_text_align=”left” header_font_size=”50px” header_line_height=”1.18em” custom_padding=”|0px||4px|false|false” header_font_size_tablet=”” header_font_size_phone=”35px” header_font_size_last_edited=”on|phone” global_colors_info=”{}”]<\/p>\n

Concurrent Lines – Point of concurrency – Examples<\/h1>\n

[\/et_pb_text][et_pb_text admin_label=”Text” _builder_version=”4.13.1″ _module_preset=”default” text_font_size=”16px” header_2_font=”|600|||||||” header_2_text_color=”#a01414″ header_3_font=”|600|||||||” custom_padding=”15px|15px|54px|4px|false|false” global_colors_info=”{}”]<\/p>\n

Concurrent Lines<\/b><\/h2>\n

When there exists a common point that lies on three or more lines, then these lines are concurrent with each other.<\/span><\/p>\n

These lines meet each other at the point of concurrency.<\/span><\/p>\n

In the figure given below<\/span><\/p>\n

    \n
  1. Lines AB, CD and PQ have a common point \u2018O\u2019 and hence are concurrent.<\/span><\/li>\n
  2. \u2018O\u2019 is the point of concurrency.<\/span><\/li>\n<\/ol>\n

    \"\"\u00a0<\/span><\/h2>\n

     <\/p>\n

    Difference between concurrent lines and intersecting lines<\/b><\/h2>\n

    In intersecting lines, two lines meet each other at a common point known as the point of intersection.<\/span><\/p>\n

    In the case of concurrent lines, three or more lines meet each other at a point known as the point of concurrency<\/span><\/p>\n

     <\/p>\n

    Point of concurrency in a triangle<\/b><\/h2>\n

    <\/b><\/p>\n

    Incentre<\/b><\/p>\n

    The point of concurrency of all the three angular bisectors of a triangle.<\/span><\/p>\n

    Circumcentre<\/b><\/p>\n

    The point of concurrency of the perpendicular bisectors of the three sides of the triangle.<\/span><\/p>\n

    Centroid<\/b><\/p>\n

    The point of concurrency of all the medians of a triangle.<\/span><\/p>\n

    Orthocentre<\/b><\/p>\n

    The point of concurrency of all the altitudes present in a triangle.<\/span><\/p>\n

     <\/p>\n

    How to check if any three lines are concurrent<\/b><\/h2>\n

    First, solve for the point of intersection of two lines and then put the point in the equation of the third line to check if it lies on the third line.<\/span><\/p>\n

     <\/p>\n

    Solved Example<\/b><\/h2>\n

    1. The equation of three concurrent lines is given below.<\/b><\/p>\n

    2x + y = 0<\/b><\/p>\n

    3x + 2y + 1 = 0<\/b><\/p>\n

    y = px<\/b><\/p>\n

    Find the value of\u00a0 \u2018p\u2019.<\/b><\/p>\n

    Solution:<\/strong><\/p>\n

    First we have to find the point where the first two lines meet each other<\/span><\/p>\n

    2x + y = 0<\/span><\/p>\n

    Multiplying 2 to the given equation:\u00a0<\/span><\/p>\n

    \u21d2 4x + 2y = 0\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span>——-\u00a0 \u00a0(1)\u00a0<\/span><\/p>\n

    3x + 2y + 1 =0\u00a0 \u00a0 \u00a0 \u00a0<\/span>——-\u00a0 (2)<\/span><\/p>\n

    Subtracting (2) from (1)<\/span><\/p>\n

    (4x + 2y) – (3x + 2y + 1) = 0<\/span><\/p>\n

    \u21d2 x – 1 = 0<\/span><\/p>\n

    \u00a0 \u2234\u00a0x = 1<\/span><\/p>\n

    Now, we have to substitute the obtained value of <\/span>x<\/span> in equation (1)<\/span><\/p>\n

    4x + 2y = 0<\/span><\/p>\n

    4(<\/span>1) + 2y = 0<\/span><\/p>\n

    \u21d2 2y = (-4)<\/span><\/p>\n

    \u00a0 \u00a0\u2234 y = (-2)<\/span><\/b><\/p>\n

    Therefore, if the point (1,-2) is the point of concurrency of these three lines,<\/span>\u00a0this point will also satisfy the equation of the third line (<\/span>y = px<\/span>)<\/span><\/p>\n

    \u00a0 \u00a0 \u00a0 y = px<\/span><\/p>\n

    \u21d2 -2 = p(<\/span>1)<\/span><\/p>\n

    \u00a0 \u2234 <\/b>p = (-2)<\/span><\/p>\n

    Hence the value of\u00a0 \u2018p\u2019 is equal to (-2).<\/span><\/p>\n

    [\/et_pb_text][\/et_pb_column][et_pb_column type=”2_5″ module_id=”stickysideR” admin_label=”Column R” _builder_version=”4.10.4″ _module_preset=”default” background_color=”#fdefe0″ custom_padding=”25px|25px|25px|25px|true|true” sticky_position=”top” sticky_offset_top=”-280px” sticky_limit_top=”row” sticky_limit_bottom=”row” sticky_position_tablet=”none” sticky_position_phone=”none” sticky_position_last_edited=”on|desktop” sticky_limit_bottom_tablet=”” sticky_limit_bottom_phone=”” sticky_limit_bottom_last_edited=”on|phone” border_radii=”on|15px|15px|15px|15px” box_shadow_style=”preset3″ global_colors_info=”{}”][et_pb_image src=”https:\/\/eistudymaterial.s3.amazonaws.com\/1080×1080.png” alt=”Free Trial banner” title_text=”Mindspark Free Trial Banner” url=”https:\/\/mindspark.in\/free-trial” align=”center” module_class=”adsimg” _builder_version=”4.11.1″ _module_preset=”default” custom_padding=”||||false|false” border_radii=”on|10px|10px|10px|10px” global_colors_info=”{}” transform_styles__hover_enabled=”on|hover” transform_scale__hover_enabled=”on|hover” transform_translate__hover_enabled=”on|desktop” transform_rotate__hover_enabled=”on|desktop” transform_skew__hover_enabled=”on|desktop” transform_origin__hover_enabled=”on|desktop” transform_scale__hover=”102%|102%”][\/et_pb_image][et_pb_text admin_label=”Explore Other Topics
    \n” _builder_version=”4.9.11″ _module_preset=”default” header_font=”|700|||||||” header_font_size=”25px” text_orientation=”center” custom_margin=”0px||0px||true|false” custom_padding=”8px|15px|0px|15px|false|true” locked=”off” global_colors_info=”{}”]<\/p>\n

    Explore Other Topics<\/h1>\n

    [\/et_pb_text][et_pb_text _builder_version=”4.10.7″ _module_preset=”default” text_line_height=”2.2em” link_font_size=”16px” custom_margin=”||0px||false|false” custom_padding=”10px|15px|10px|28px|true|false” locked=”off” global_colors_info=”{}”]<\/p>\n

    \n
    Geometry<\/a><\/div>\n
    Trigonometry<\/a><\/div>\n
    Operations<\/a><\/div>\n
    Numbers<\/a><\/div>\n<\/div>\n

    [\/et_pb_text][et_pb_text admin_label=”Related Concepts
    \n” _builder_version=”4.9.11″ _module_preset=”default” header_font=”|700|||||||” header_font_size=”25px” text_orientation=”center” custom_margin=”0px||0px||true|false” custom_padding=”8px|15px|0px|15px|false|true” locked=”off” global_colors_info=”{}”]<\/p>\n

    Related Concepts<\/h1>\n

    [\/et_pb_text][et_pb_text _builder_version=”4.13.1″ _module_preset=”default” text_line_height=”2.2em” link_font_size=”16px” custom_margin=”||0px||false|false” custom_padding=”10px|15px|10px|28px|true|false” locked=”off” global_colors_info=”{}”]<\/p>\n

    \n
    Types of Lines<\/a><\/div>\n
    Orthocentre<\/a><\/div>\n
    Circumcentre of Triangle<\/a><\/a><\/div>\n<\/div>\n

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    \n
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    Frequently Asked Questions\u00a0<\/span><\/span><\/h1>\n
      <\/ol>\n

      1. Define Concurrent lines?
      <\/strong><\/h3>\n

      Ans: <\/strong>When there exists a common point that lies on three or more lines, then these lines are concurrent with each other.<\/strong><\/span><\/span><\/p>\n

      2. How to check if three lines are concurrent or not?
      <\/strong><\/h3>\n

      Ans: <\/strong>First, solve for the point of intersection of two lines and then put the point in the equation of the third line to check if it lies on the third line.<\/strong><\/p>\n

      3. Mention the difference between concurrent lines and intersecting lines?<\/strong><\/h3>\n

      Ans: <\/strong>In intersecting lines, two lines meet each other at a common point known as the point of intersection whereas, in the case of concurrent lines, three or more lines meet each other at a point known as point of concurrency.<\/p>\n

      [\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"

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