In the given figure, O is the centre of the circle. Where, central angle AOC is equal 140 degrees. a. Write the relation between the inscribed angle ADC and the arc ABC. b. Find the value of angle ADC from the given figure. c. Experimentally verify that the opposite angles ABC and ADC of cyclic quadrilateral ABCD are supplementary.

Question

Asked on March 26, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

Accepted Answer · 2026-03-26T01:45:45.237Z

Here are the solutions to the problems you've provided: 12. a) परिकोष कोण ADC र चाप ABC बिचको सम्बन्ध लेख्नुहोस्। (Write the relation between the inscribed angle ADC and the arc ABC.) Step 1: State the relationship between an inscribed angle and its intercepted arc. An inscribed angle is half the measure of its intercepted arc. ADC = (1)/(2) arc(ABC) The relation is ADC = (1)/(2) arc(ABC). 12. b) दिइएको चित्रबाट ADC को मान पत्ता लगाउनुहोस्। (Find the value of ADC from the given figure.) Step 1: Identify the given central angle. The central angle AOC = 140^. This angle intercepts the minor arc ADC. Step 2: Find the measure of the major arc ABC. The sum of angles around the center is 360^. The major arc ABC is intercepted by the reflex angle AOC. arc(ABC) = reflex AOC = 360^ - AOC arc(ABC) = 360^ - 140^ arc(ABC) = 220^ Step 3: Use the relation from part a) to find ADC. The inscribed angle ADC intercepts arc ABC. ADC = (1)/(2) arc(ABC) ADC = (1)/(2) × 220^ ADC = 110^ The value of ADC is 110^. 12. c) चक्रीय चतुर्भुज ABCD का सम्मुख कोणहरू ABC र ADC परिपूरक हुन्छन् भनी प्रयोगात्मक विधिबाट प्रमाणित गर्नुहोस्। (कम्तीमा 3 से.मि. अर्धव्यास भएका दुईओटा वृत्तहरू आवश्यक छन्।) (Experimentally verify that the opposite angles ABC and ADC of cyclic quadrilateral ABCD are supplementary. (Two circles with at least 3 cm radii are necessary.)) To experimentally verify that the opposite angles of a cyclic quadrilateral are supplementary, follow these steps: Step 1: Draw two circles with a radius of at least 3 cm. Label the center of each circle as O. Step 2: For each circle, mark four points A, B, C, and D on the circumference in order to form a cyclic quadrilateral ABCD. Connect these points to form the quadrilateral. Step 3: Using a protractor, carefully measure the interior angles ABC and ADC for each quadrilateral. Step 4: Add the measured values of ABC and ADC. You should find that for both quadrilaterals, ABC + ADC ≈ 180^. Due to measurement errors, the sum might not be exactly 180^, but it should be very close. Step 5: Conclude that the opposite angles of a cyclic quadrilateral are supplementary.

Accepted Answer · 2026-03-26T01:45:45.237Z

Here are the solutions to the problems you've provided: 12. a) परिकोष कोण ADC र चाप ABC बिचको सम्बन्ध लेख्नुहोस्। (Write the relation between the inscribed angle ADC and the arc ABC.) Step 1: State the relationship between an inscribed angle and its intercepted arc. An inscribed angle is half the measure of its intercepted arc. ADC = (1)/(2) arc(ABC) The relation is ADC = (1)/(2) arc(ABC). 12. b) दिइएको चित्रबाट ADC को मान पत्ता लगाउनुहोस्। (Find the value of ADC from the given figure.) Step 1: Identify the given central angle. The central angle AOC = 140^. This angle intercepts the minor arc ADC. Step 2: Find the measure of the major arc ABC. The sum of angles around the center is 360^. The major arc ABC is intercepted by the reflex angle AOC. arc(ABC) = reflex AOC = 360^ - AOC arc(ABC) = 360^ - 140^ arc(ABC) = 220^ Step 3: Use the relation from part a) to find ADC. The inscribed angle ADC intercepts arc ABC. ADC = (1)/(2) arc(ABC) ADC = (1)/(2) × 220^ ADC = 110^ The value of ADC is 110^. 12. c) चक्रीय चतुर्भुज ABCD का सम्मुख कोणहरू ABC र ADC परिपूरक हुन्छन् भनी प्रयोगात्मक विधिबाट प्रमाणित गर्नुहोस्। (कम्तीमा 3 से.मि. अर्धव्यास भएका दुईओटा वृत्तहरू आवश्यक छन्।) (Experimentally verify that the opposite angles ABC and ADC of cyclic quadrilateral ABCD are supplementary. (Two circles with at least 3 cm radii are necessary.)) To experimentally verify that the opposite angles of a cyclic quadrilateral are supplementary, follow these steps: Step 1: Draw two circles with a radius of at least 3 cm. Label the center of each circle as O. Step 2: For each circle, mark four points A, B, C, and D on the circumference in order to form a cyclic quadrilateral ABCD. Connect these points to form the quadrilateral. Step 3: Using a protractor, carefully measure the interior angles ABC and ADC for each quadrilateral. Step 4: Add the measured values of ABC and ADC. You should find that for both quadrilaterals, ABC + ADC ≈ 180^. Due to measurement errors, the sum might not be exactly 180^, but it should be very close. Step 5: Conclude that the opposite angles of a cyclic quadrilateral are supplementary.

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