Question

In the given figure, BOC is a diameter of a circle and AB = AC. Then, ∠ABC = ?

$\textit{please solve with full explanation }$​

Answer 1

Answer:

45

Step-by-step explanation:

we know angle in a semi circle is 90

that means angle BAC=90

and given that AB=AC

that means it's an isosceles triangle

so remaining angles will be equal and add up-to 90

so 2x=90

x=45

so angle ABC=45

Answer 2

Given :- In the given figure, BOC is a diameter of a circle and AB = AC.

To Find :- ∠ABC = ?

Concept used :-

• The angle at the circumference in a semicircle is 90° .
• Angle opposite to equal sides of a ∆ are equal in measure .
• Sum of all three angles of a ∆ is equal to 90° .

Solution :-

In ∆ABC we have,

→ ∠BAC = 90° { Angle at the circumference in a semicircle .}

→ AB = AC { given }

So,

→ ∠ABC = ∠ACB { Angle opposite to equal sides of a ∆ are equal in measure . }

then,

→ ∠ABC + ∠ACB + ∠BAC = 180° { Angle sum property. }

→ ∠ABC + ∠ABC + 90° = 180°

→ 2•∠ABC + 90° = 180°

→ 2•∠ABC = 180° - 90°

→ 2•∠ABC = 90°

dividing both sides by 2,

→ ∠ABC = 45° (Ans.)

Hence, ∠ABC is equal to 45° .

Learn more :-

In the figure along side, BP and CP are the angular bisectors of the exterior angles BCD and CBE of triangle ABC. Prove ∠BOC = 90° - (1/2)∠A .

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