Question

9. ಮೂಲ ಸಮಾನುಪಾತತೆಯ ಪ್ರಮೇಯವನ್ನು ನಿರೂಪಿಸಿ,
10. Sm ತ್ರಿಜ್ಯವಿರುವ ವೃತ್ತಕ್ಕೆ ಕೇಂದ್ರದಿಂದ 13mದೂರದಲ್ಲಿರುವ ಒಂದು ಬಿಂದುವಿನಿಂದ ಎಳೆದ ಸ್ಪರ್ಶಕದ ಉದ್ದವನ್ನು
ಕಂಡುಹಿಡಿಯಿರಿ.​

Answer 1

The basic theorem of proportionality was introduced by the famous Greek mathematician Thales, therefore it is also called Thales' theorem. According to him, for any two right-angled triangles, the ratio of any two corresponding sides is always the same. Based on this concept, he gave the Basic Proportionality Theorem (BPT). This concept was introduced in similar triangles. If two triangles are similar, then

• i) Corresponding angles of both triangles are equal
• ii) Corresponding sides of both triangles are proportional to each other

The radius of the circle and the tangent and the distance from the center to the tangent combine to form right triangles with the distance from the center to the point of the tangent as the hypotenuse

So to Pyatagoreon's theorem

$(13)^2=(12)^2+x^2\\169-144=x^2\\x^2=25\\x=5$

Hence the length of the tangent is $5$cm.

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Answer 2

Explanation:

Sm ತ್ರಿಜ್ಯವಿರುವ ವೃತ್ತಕ್ಕೆ ಕೇಂದ್ರದಿಂದ 13mದೂರದಲ್ಲಿರುವ ಒಂದು ಬಿಂದುವಿನಿಂದ ಎಳೆದ ಸ್ಪರ್ಶಕದ ಉದ್ದವನ್ನು

ಕಂಡುಹಿಡಿಯಿರಿ.