To find: In given figure, if a line from center O, perpendicular to tangent, bisects its corresponding chord.
Answer to Problem 23WE
Given figure suggest the statement that if a perpendicular is drawn on point of contact of tangent on it, it bisects the chord of another concentric
Explanation of Solution
Given information: In below given figure,
Concept used: (i) Any line from center to point of contact of tangent on it, is perpendicular on it.
(ii) Using HL congruency, in two right
Calculation: In given figure,
Given :
To prove :
Construction: Draw perpendicular
Proof: In right triangles
So, by HL (Hypotenuse-leg) congruency, these two triangles are congruent. Hence, by CPCT (corresponding parts of congruent triangles) property,
Conclusion: Thus, It proves that any perpendicular from the center of a circle to its chord, always bisects this chord.
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McDougal Littell Jurgensen Geometry: Student Edition Geometry
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