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AD is a diameter of circle centre O. B is a point on the circumference. BC ot AD. B1 = 41^. Calculate the size of: a) B2 b) D

April 21, 2026Mathematics

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5. Given: AD is a diameter of circle centre O. B is a point on the circumference. BC $\perp$ AD. $\hat{B_1} = 41^\circ$ .
Calculate the size of:

$\hat{B_2}$

$\hat{D}$

Analyze the given information and diagram.
Let E be the intersection point of BC and AD.
Given $\angle BAC = \hat{B_1} = 41^\circ$ .
Given BC $\perp$ AD, so $\angle AEB = 90^\circ$ .
AD is a diameter, so $\angle ABD = 90^\circ$ (Angle in a semicircle).
Calculate $\hat{B_2}$ .
In $\triangle ABE$ :
$\angle ABE = 180^\circ - \angle BAE - \angle AEB$ $\angle ABE = 180^\circ - 41^\circ - 90^\circ$ $\angle ABE = 49^\circ$
We know that $\angle ABD = 90^\circ$ .
Also, $\angle ABD = \angle ABE + \angle EBD$ .
$90^\circ = 49^\circ + \angle EBD$ $\angle EBD = 90^\circ - 49^\circ$