In the given figure, A B C D E is a pentagon inscribed in a circle such that A C is a diameter and side B C ∥ A E . If ∠ B A C = 50 ° , find giving reason ∠ A C B .

We have, In the given figure, A B C D E is a pentagon inscribed in a circle such that A C is a diameter and side B C ∥ A E . If ∠ B A C = 50 ° , Now, ∠ A B C = 90 ° (Angle in a semicircle) In ∆ A B C , ∠ A B C + ∠ B A C + ∠ A C B = 180 ° (angle sum property of a triangle) 90 ° + 50 ° + ∠ A C B = 180 ° 140 ° + ∠ A C B = 180 ° ∠ A C B = 180 ° - 140 ° ∠ A C B = 40 °

In the given figure, A B C D E is a pentagon inscribed in a circle such that A C is a diameter and side B C ∥ A E . If ∠ B A C = 50 ° , find giving reason ∠ E D C .

Given, Since A C is a diameter and angle in a semi-circle is right angle ∠ B = 90 ° And, ∠ A C B = 180 ° - ∠ B - ∠ B A C = 180 ° - 90 ° - 50 ° = 40 ° Also, B C ∥ A E ⇒ ∠ E A C = ∠ A C B = 40 ° [alternate interior angles] In cyclic quadrilateral A C D E , ∠ E A C + ∠ E D C = 180 ° [opposite angles are supplementary] ⇒ 40 ° + ∠ E D C = 180 ° ⇒ ∠ E D C = 180 ° – 40 ° = 140 ° Hence, ∠ E D C = 140 °

In the given figure, A B C D E is a pentagon inscribed in a circle such that A C is a diameter and side B C ∥ A E . If ∠ B A C = 50 ° , find giving reason ∠ B E C

Given figure: Join B E and E C Given, ∠ B A C = 50 ° So, ∠ B E C and ∠ B A C as they are angles in same segment formed by chord B C . So, they are equal. ∠ B E C = 50 ° .

E M B I B E

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Circles>ICSE-2020>Q 12

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10th ICSE

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In the given figure $T P$ and $T Q$ are two tangents to the circle with centre $O$ , touching at $A$ and $C$ respectively. If $∠ B C Q = 55 °$ and $∠ B A P = 60 °$ , find $∠ A O C .$

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Important Questions on Circles

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10th ICSE

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 15 - Circles>ICSE-2020>Q 13

In the given figure $T P & T Q$ are two tangents to the circle with centre $O$ , touching at $A & C$ respectively. If $∠ B C Q = 55 ° & ∠ B A P = 60 °$ , find $∠ A T C$ in degrees.