CBSE Class 10 Answered
Prove that the tangent drawn at the mid-point of an arc of a circle is parallel to the chord joining the end points of the arc.
Asked by satapathy99 | 16 Mar, 2015, 11:16: PM
![](https://images.topperlearning.com/topper/tinymce/imagemanager/files/vijay/Va10.jpg)
![In space the space figure comma space straight C space is space the space midpoint space of space the space minor space arc space PQ comma straight O space is space the space centre space of space the space circle space and space AB space is space tangent space to space the space circle space through space point space straight C. We space space have space to space show space the space tangent space drawn space at space the space midpoint space of space the space ars space PQ space of space straight a space circle space is space parallel space to space the space chord space joining space the space end space points space of space the space arc space PQ. straight i. straight e. space We space will space show space PQ space vertical line vertical line space AB. It space is space gien space that space straight C space is space midpoint space of space the space arc space PQ. So comma space arc space PC space equals space arc space CQ rightwards double arrow space PC equals CQ This space shows space that space increment PQC space is space an space isosceles space triangle. Thus comma space the space perpendicular space bisector space of space the space side space PQ space of space increment PQC space passes space through space vertex space straight C. The space perpendicular space bisector space of space straight a space chord space passes space through space the space centre space of space the space circle. So space the space perpendicular space bisector space of space PQ space space passes space through space the space centre space straight O space of space the space circle. Thus space perpendicular space bisector space of space PQ space passes space through space the space points space straight O space and space straight C. rightwards double arrow PQ perpendicular OC AB space is space the space tangent space to space the space circle space through space the space point space straight C space on space the space circle. rightwards double arrow AB perpendicular OC The space chord space PQ space and space the space tangent space PQ space of space the space circle space are space perpendicular space to space the space same space line space OC. therefore PQ space vertical line vertical line space AB](https://images.topperlearning.com/topper/tinymce/integration/showimage.php?formula=1d7d62e3ed5f5a86f6da4bfb6bf98e87.png)
Answered by Vijaykumar Wani | 17 Mar, 2015, 11:22: AM
Application Videos
Concept Videos
CBSE 10 - Maths
Asked by jennyy | 26 Mar, 2022, 08:41: PM
CBSE 10 - Maths
Asked by amikasangma080 | 11 Oct, 2021, 06:14: PM
CBSE 10 - Maths
Asked by muskanmahek2411 | 08 Oct, 2021, 10:48: PM
CBSE 10 - Maths
Asked by anishasheoran372 | 13 Jul, 2021, 09:33: AM
CBSE 10 - Maths
Asked by anushkasingh260805 | 20 Dec, 2020, 07:22: PM
CBSE 10 - Maths
Asked by anjalirajp004 | 22 Sep, 2020, 08:17: AM
CBSE 10 - Maths
Asked by rashikediadelhi | 21 Sep, 2020, 09:02: AM
CBSE 10 - Maths
Asked by prasutally | 26 May, 2019, 08:23: AM
CBSE 10 - Maths
Asked by prasutally | 26 May, 2019, 08:22: AM
CBSE 10 - Maths
Asked by kamatshantanu | 08 May, 2019, 11:39: AM