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(A) Given that $AB$ is a chord of a circle with centre $P$. Point $C$ is a point on the major arc $AB$.According to the circle theorem,the angle subte

Vedclass · Accepted Answer

$45^{\circ}$ and $90^{\circ}$

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(A) Given that $AB$ is a chord of a circle with centre $P$. Point $C$ is a point on the major arc $AB$.According to the circle theorem,the angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.Therefore,$\angle APB = 2 \angle ACB$.Given that $\angle ACB + \angle APB = 135^{\circ}$.Substituting $\angle APB = 2 \angle ACB$ in the given equation:$\angle ACB + 2 \angle ACB = 135^{\circ}$$3 \angle ACB = 135^{\circ}$$\angle ACB = \frac{135^{\circ}}{3} = 45^{\circ}$.Now,calculating $\angle APB$:$\angle APB = 2 	imes 45^{\circ} = 90^{\circ}$.Thus,$\angle ACB = 45^{\circ}$ and $\angle APB = 90^{\circ}$.

$AB$ is a chord of a circle with centre $P$. Point $C$ is a point other than $A$ and $B$ on the major arc $AB$. If $\angle ACB + \angle APB = 135^{\circ}$,then find $\angle ACB$ and $\angle APB$.

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